It is Friday night in one of the three bars in the port of Nuuk, a town closer to Baffin Island off Canada than to anywhere in Europe. This is so far north that faded unopened letters from around the world addressed to "Father Christmas, Greenland, The North Pole" fill a giant, red, glass- fronted mailbox by the post office across the road.
Nuuk's 13,000 residents have snowmobiles instead of cars, because there are no roads. The white desert of icecap and permafrost stretches out beyond Nuuk for 1,500 miles, and Greenlanders, like Smilla Jaspersen in the Peter Hoeg bestseller, are born with "a sense of snow". But here in the capital, the Danish-brewed beer is ordered in Danish from a Danish bartender. Payment is in Danish crowns.
The Spar supermarket sells crisps made in Denmark, biscuits stamped "By appointment to the Royal Danish Court" and radishes grown in Danish soil. Danish newspapers and magazines about the Danish royals fill the racks at the checkout.
"Yes, we are still part of the Kingdom of Denmark," admits Greenland's Prime Minister, Jonathan Motzfeldt. "That is our blessing and our problem." After 250 years of direct Danish rule, Greenlanders won a large measure of devolved government in 1979. In 1985, after 12 years inside the European Union, they voted to leave. Greenland remains the only place ever to have withdrawn from the bloc.
Remaining under the thumb of Brussels made no sense, says Mr Motzfeldt. "We are 3,000 kilometres from Europe. Ethnically and culturally, we are different. Canada and the US are our nearest neighbours - we are part of the American continent." Fish is Greenland's only industry and fear of EU fishing quotas motivated the decision.
Mr Motzfeldt, a former Lutheran priest, his six ministers and the 31 MPs of the Landsting (parliament) run Greenland's education, health, housing, environment, its national church and, of course, its fisheries. But the biggest island in the world, five times the size of France, is still joined to Denmark by an umbilical cord. Copenhagen controls foreign policy, defence, justice and monetary policy.
The "blessing" the Prime Minister pragmatically talks of is the "block grant", a lifeline of almost Dkr3bn (pounds 270m) a year, nearly 60 per cent of the total national income. But the reliance goes beyond money: half of all civil servants in the Nuuk administration are Danish, the schools are filled with Danish teachers, the hospitals staffed by Danish doctors and nurses. "Every system that works here is Danish," says a reporter at Sermitsiak, a local newspaper.
But last week Denmark voted to strengthen ties with the EU, forcing the 55,000 people in Greenland's frozen wastes to think again about full independence. Greater self-reliance is unthinkable, notes an aide to the Prime Minister - "unless we find oil". The search for minerals thought to lie untapped in and around Greenland has now become more urgent.
Greenlanders are still coming to terms with the traumatic effects of European colonisation. After thousands of years of self-sufficiency in the earth's most hostile climate, the 1960s brought "modernisation", which involved resettlement to the towns, suppression of the Inuit language and the dispatch of thousands of children to school in Denmark.
In Copenhagen, the average Dane will tell you they know little except that the Greenlanders are "special" people who drink a lot. Ecologically minded Danes come to live here in search of "nature" and the Inuit way of life. But most Inuits live in Soviet-style blocks of flats, and their children wear baseball caps and have in-line skates. The "Disco Palace" in Nuuk was humming on Friday night; the town's only record store has a good stock of Dolly Parton, but not a lot of traditional drum dancing music.
Danish involvement is not all altruism: the US air base at Thule in north- west Greenland, opened during the Second World War, saves Denmark millions of crowns in Nato spending. The Danes can also expect to reap their investment several times over if oil exploration off the west coast produces results next year. The Greenlanders will decide which companies get prospecting licences, but by threatening to cut support, the Danes have secured legal entitlement to half of the income.
Aqqaluk Lynge, an Inuit leader, recalls with some bitterness his own experience after being plucked from a hunting family to be sent to board with a Danish family at the age of 13 in 1961. "I knew we were different," he said, "when I kicked the dog and they beat me." Greenlanders rebelled by "making fun of them" and giving them hurtful nicknames. "That is the way our parents fought the colonists, and we still do it."
Yet, Queen Margrethe gets a rousing reception any time she sets foot in this part of her realm, and Aqqaluk Lynge has a picture on his wall of Crown Prince Frederic. He laughs sheepishly: "Oh that, I forgot to take it down." But then he adds: "I like him. When he came here a few years ago, he went seal hunting."