In the cross-hairs of the telescopic sight on my high-powered rifle is a 900lb beast with a vast head, shaggy body and antlers 5ft wide. I am deep in the Alaskan wilderness. I am incredibly cold, having just waded through a freezing river, and I am very slightly alarmed by the large black bear watching us hungrily from the nearby hillside. I am hunting for moose. Strictly speaking, I am hunting for Sarah Palin, by hunting for moose.

Palin's taste for moose-hunting is a central plank of her political personality. It is almost obligatory, when writing about the Alaska Governor and Republican vice-presidential candidate, to refer to her as the “gun-toting, moose-hunting mother-of-five”. Palin is the first candidate in history who tracks, kills, guts, skins, cooks and then eats big game, and also wears high heels, though not, surely, at the same time.

Palin's reputation as a moose-hunter is central to her appeal as a frontierswoman, an appeal that has transformed the presidential race. If John McCain gets to the White House he will owe it, in part, to a dead moose. A photograph of Palin sitting in the bloodstained snow, gun in hand, alongside the carcass of a large animal killed by her own fair hand, has been published in virtually every newspaper in the world: it is an image that makes Republicans, hunters and gun-owners very happy; it is an image that makes many environmentalists, liberals, gun-control advocates and Democrats extremely angry, and very nervous.

So what is moose-hunting? How difficult, natural, barbaric, traditional, valuable or weird is it? What does moose taste like? I have come to Moose Pass on the Kenai Peninsular, an impossibly beautiful and empty expanse of forest, river and mountain in southern Alaska, to find out.

My guide to the mysteries of moose hunting is Dan Rinella, a charming and unshaven 36-year-old biologist from the University of Alaska. Dan is “the finest moose-hunter in Alaska”, according to my contact at the Alaska Conservation centre. He is also, somewhat surprisingly, a Democrat. Indeed, he may be the only Democratic moose-hunter in Alaska.

As we motor through the night to the Kenai Peninsular in a huge pickup truck with an 18ft aluminium boat rattling behind, Dan explains what is about to happen. We will drive about 100 miles from Anchorage, launch the boat on Trail Lake, and then motor upriver for about two hours until we reach Moose Pass in the interior. We will then climb to a higher vantage point and wait for the moose to arrive. If we see the right sort of moose we will shoot it through the lungs. After that we will remove the hide, saw off the head, remove the internal organs and anus, chop off the legs below the knee, and divide the body into quarters. We will then pack the meat into backpacks and stagger bloodily back to the boat. Since there could be up to 600lb of meat, this might take several days, but we will need to get it done before the bears and wolves arrive. Some time later Dan's wife, Corinna, will make us a moose supper.

Dan says cheerily that he has a knife and saw, so we can both do the field-dressing, and two backpacks. Dan, however, will pull the trigger: the only shooting I plan to do is with a video camera.

What, I ask, is the right sort of moose? Dan explains. We cannot shoot cow moose or their calves. We can shoot only bull moose that are very large, with antler racks at least 50 inches across, or yearling bulls, with small horns that are spikes or forked. Every licensed Alaskan hunter may take one legal bull per year during the brief autumn hunting season. There are an estimated 175,000 moose in Alaska, but in the most remote areas they may be as sparse as one to every 30 square miles. We are setting out on the very last day of the season. “I'm warning you,” says Dan. “We are very, very unlikely to shoot a moose.”

The sun is rising as we reach Trail Lake. The spectacle, as the dawn creeps up the snow-covered mountain, is breathtaking. Dan has lent me jackets, waterproofs and boots, but the cold is vicious. He carries a Winchester 300 Magnum with elaborately carved stock, and a sniper scope. I carry the Oreo cookies, for elevenses.

As we reach the mouth of Trail Creek, the boat runs aground. We get out and push, boots sinking into deep, slurping mud. On either bank, blueberries, alder, spruce and fireweed grow in profusion. The mountain rises sheer, punctuated by glaciers. It is like Scotland on steroids.

Finally we park the boat, wade through a marsh, and scramble up on to a rocky ledge, about 200ft above the valley. Dan surveys the area through binoculars. “They're big, but they can hide,” he says. “Often, the only thing you spot is the antlers, moving above the brush.” The old Alaska railroad runs through the valley, on wooden struts. It is the only sign that humanity has ever been here before.

Dan points out a bear and its cub, moving across the snow line. “If we run into a grizzly, and it attacks, just play dead,” Dan explains. I explain to Dan that if a bear comes anywhere near me, I expect him to shoot it immediately, while I run screaming back to the boat.

Freezing mud has seeped down into my socks. Sarah Palin has gone up in my estimation. The Governor of Alaska learnt to handle a gun at 8 and shot her first moose at 10 years old. The animal has become the symbol of her campaign: “Mother, moose-hunter, maverick,” is her chosen self-description. Immediately after the Republican convention, she and McCain stopped at an ice-cream shop in Cedarburg, Wisconsin, so that she could order a scoop of “Moosetracks” - vanilla ice-cream with peanut butter cups and fudge.

Certain Republicans become weak-kneed at Palin's huntswoman qualities. She is, declared Senator Fred Thompson, “the only nominee in the history of either party who knows how to properly field-dress a moose ... with the possible exception of Teddy Roosevelt”.

Dan, however, is unimpressed. “I don't think Sarah Palin hunts moose like we are doing now. I think she drives in an all-terrain vehicle to somewhere convenient, shoots a moose, then someone else cuts it up and brings it back.”

Not all moose-hunters are equal. Some, it seems, simply drive along the interstate and shoot one if they see one: this is called moose-cruising. Others do it in style. The hardcore hunters hire planes or helicopters and fly to the most inaccessible spots, where they camp for up to two weeks, shooting moose and spending at least $10,000 for the privilege. “This is the only way to hunt moose, on foot,” insists Dan.

Suddenly he tenses, “Shit, man, look at that, there he is.” In the far distance, a bull moose is moving across the valley floor. With the naked eye it is barely a blur, but through the telescopic sight it is clearly visible, stepping with lolling strides, pausing to snatch at a bush, an almost impossible spread of antlers on its horse-like head - the largest deer in the world.

The animal is too distant to attempt a shot. We scramble back into the boat and head upriver, nearer to where the moose was feeding. Dan thinks that he has spotted another, even larger, moving towards the same spot. On a nearer ledge, beneath a large spruce, we take up another lookout position, but the moose have vanished. The two enormous creatures have simply disappeared into the undergrowth.

Moose are short-sighted and usually docile creatures, although cows with calves can be aggressive, and more people are attacked by angry moose in Alaska than by bears. Their natural predators being bears and wolves, a bull moose will often let a human being come within 20ft. Henry David Thoreau, the American writer and naturalist, described hunting moose as “like going out by night to some woodside pasture and shooting your neighbour's horses”.

It is not that easy: moose-hunting takes skill, patience and antifreeze in the blood. Only one in three moose-hunters bags a moose, and many hunt every day of the season. Yet moose-hunting is considered almost a birthright in Alaska. This is not a rich state, and for many families a moose in the freezer represents a huge nutritional boon for the winter months.

Dan is defensive when I refer to moose-hunting as a “blood sport”. “I find that term demeaning. This is about food. Is it better that I shoot a moose, or import 600lb of beef from the lower 48 [the term used by Alaskans for the rest of America]?” For Sarah Palin, however, moose-hunting is a matter of politics, not subsistence. Her taste for moose stew sends a direct message to voters, even those suburbanites who would never consider killing any animal, let alone a moose. It is an image that harks back to a pioneering past, a time when America was still young and empty, abundant in nature and opportunity.

We wait in Moose Pass, scanning the land, until the sun begins to slant down the valley. The moose have gone. My circulation has gone. It is time to go. Trudging back, Dan is philosophical. “I'm glad we didn't get one today. Preserves a little of the moose mystique.” I am glad too.

In the petrol station on the way back to Anchorage, there is a pickup and trailer filled with hunters, and a huge, dead moose. The severed legs stick up and the decapitated head has been arranged to look out over the back of the trailer, its huge lips black and its eyes closed. The brake lights cast the animal's long, dour face in a red glow as the truck moves off: it is a sight at once eerie, impressive and revolting, the dignified creature I had seen a few hours early reduced to a gory trophy.

Thoreau, who witnessed the killing and field-dressing of a moose in 1853, was revolted. “Nature looked sternly upon me on account of the murder of the moose,” he wrote. “A tragical business it was; to see that still warm and palpitating body pierced with a knife... and the ghastly naked red carcass appearing from within its seemly robe.”

It might seem bizarre that moose-hunting should suddenly loom large in the US election, a symbol of pioneering independence to some and savage bloodlust to others. But then, this harmless, majestic beast has always been exploited by man, for better and for worse: for food, for clothing, for sport, and now for presidential politics.

How does it taste: cooking with moose

To eat moose you have to kill it yourself, or have someone kill it for you, since the sale of wild game is illegal in the US and moose meat cannot be bought in shops or served in restaurants.

Luckily, Dan Rinella has plenty of moose in his freezer from last year's hunt: tonight we are having barbecued moose steaks.

Just as the moose is perfectly adapted to its environment in the wild, it is also infinitely adaptable on a plate: pizza topped with ground moose is popular in Alaska, as is moose stroganoff and moose bolognaise, known as Mooseghetti. Sarah Palin lists moose stew (see recipe below) and moose burgers among her favourite foods.

Connoisseurs say that boiled moose nose, roughly the size of a football on a larger bull, is a particular delicacy.

Moose hunting websites describe the meat as dense and coarse-grained, leaner than beef and extremely healthy. What wine does one drink with moose steak? I consult Pete at the Oak Barrel liquor store in downtown Anchorage. “Moose can be pretty tough, depending how it's cooked, but it's got a rich flavour. You want something pretty robust to go with it, like a red Zinfandel.”

Armed with a bottle of Pete's most muscular Zinfandel, I head to Dan's home, where the barbecue is on and Corinna is roasting vegetables grown in their backyard.

The moose steak is delicious, pink and succulent, like a cross between sirloin and venison, with a delicious peppery crust. I have eaten various odd things over the years: rattlesnake, kangaroo and once, by mistake, owl. All, predictably, tasted of chicken.

Moose doesn't taste remotely of chicken: it takes, oddly enough, of the American wilderness.

Moose stew à la Palin

Ingredients

2lb moose, cubed

3 slices bacon, cut up

4 onions, quartered

4 potatoes, quartered

1 packet fresh or frozen green beans

3 bay leaves

4 carrots, sliced

1 packet fresh or frozen peas

1 tin tomato juice

Method

Brown bacon in heavy pan. Add moose and brown on all sides. Add onions and sauté. Add all remaining ingredients and simmer for 1 hour or until flavours are mixed and vegetables and meat are tender. Remove bay leaves.

Times recommends

• Prince Philip attacks big families
• Take a dip in Dubai-on-Thames
• Eco Worrier: How can I persuade my husband to use a push mower?