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You won't dip your toe in the sea, but you'll still get a tan

It's not an obvious choice, says Mark Steel, but Greenland has its attractions – friendly people, great views, and a polar bear nailed to every wall

'What you going there for?" That's the start of Greenland holiday fun, being asked that question over and over again, by neighbours, the man who arranges your travel insurance, the woman you buy the Big Issue from, all of whom look as puzzled as if you'd said you'd booked a week at an industrial estate outside Ipswich to go fork-lift truck spotting.

The man in the shop that sold coats in Croydon asked, "You need it for where?" "Greenland," I told him again.

"Never heard of it," he said.

"You must have heard of it, it's way up North," I said.

"Oh right, in the Lake District." Then his assistant snapped, "No, you idiot, it's where Father fucking Christmas comes from."

"I'll Google it when I get in," he said.

I've no idea why I've always been fascinated by Greenland. It may be the remoteness; for example one per cent of the country's entire population lives in one apartment block in the capital. That population is 56,000, fewer than the average crowd at Old Trafford. But the country is 10 times bigger than Britain, most of it is uninhabitable pack ice, and the far end is only 500 miles from the North Pole.

This gives the place an endearing peculiarity. The Prime Minister, Kuupik Kleist, is a singer who still releases CDs and is known as "Greenland's Leonard Cohen". The National Anthem is called "Nunarput utoqqarsuanngoravit". And its eccentricity extends to the notes provided by Discover the World, the tour operator I travelled with, for visitors to the island.

Among the tips the company provides is one, under a heading "Clothing", that says: "Greenland's dress code is casual." Unlike Finland, I suppose, where they don't let you in without a bow tie. And there's information on how to reach the Ammassalik mountain, that says: "Follow the path, then 200 metres after the crossing, change direction." Any direction presumably, as all directions are pretty much the same. In the advice on wrapping up warm, as well as recommending lots of layers, plus scarves, boots, and woolly hats, they tell you: "While you won't get a Mediterranean tan, you can come back a strange shade of brown."

And my family were travelling to the less fashionable East Greenland, where the people speak the unwritten East Greenlandic, separate from the official West Greenlandic, and are generally looked down upon by West Greenlanders who, if you told them you were going to East Greenland, would probably say: "What you going there for?"

This all made even the arrival at Kulusuk an adventure, the opposite of a typical airport with officey carpeted corridors, adverts for jewellery, and Subway sandwiches. Instead, you descend between gloriously bleak mountains across icebergs scattered like discarded Polystyrene at a festival of litter, and you land on an unpaved, gravelly runway, at which point my teenage son yelled: "But Dad – there's absolutely nothing here."

Then you walk through the terminal, which is smaller than the average Greggs the bakers, and spot an unusual airport feature, a vast polar bear nailed to the wall. To be fair, it was just the fur and head, an Arctic version of a colonial tiger rug. But when you arrive at the Hotel Kulusuk, about 400 yards from the airport along a dusty track, the first thing you see is a vast polar bear nailed to the wall.

We saw another one later, in the hotel at Tasiilaq, and began to wonder whether every public building in East Greenland has a polar bear nailed to the wall; the Post Office, garden centres, the dentist. If an East Greenlander came to Britain they'd think: "The deprivation here is dreadful. Most of the houses don't even have a polar bear nailed to the wall."

Around four minutes after landing, you arrive at Hotel Kulusuk, which is unexpectedly like a hotel, with an affable young Danish manager called Jesper, an impressive fishy Arctic buffet, and rooms with a shower and a television and heating, so you're pleasantly reassured but disappointingly comfortable, because you realise this doesn't quite make you Captain Oates.

Still, you are unmistakably in Greenland, because out of the window, about 50 yards away, are icebergs. Before going, I was slightly worried we wouldn't see any, the way you'd fear you won't see a rhino on a safari. But there are millions of them, each one a sculpture, many of them making implausible shapes, with columns and arches and if you look hard enough there are probably aqueduct icebergs and Colosseum icebergs and an iceberg in the shape of the ring road around Norwich.

But the really extraordinary part is when you wander about for a while, come back, and they're all different. It's as if a holy butler delivers a new set every two hours. Maybe the hotel should get someone to pull your curtains each morning and say: "This morning's icebergs, sir." Then at certain points, when the tide is at its most energetic, you can watch them in their hundreds drifting together, as if they're marching steadily and with a purpose, like football fans on the way to the ground or 1950s shipbuilders heading for their shift.

This is a scene you can watch and watch until you drift into an iceberg trance, which you're periodically jolted from when two collide with a calamitous crunch, and you expect the one in front to angrily ask for the one behind's insurance details. Or better still, one of them might implode. There was a huge one that collapsed into four quarters, about five yards from where we were standing, while a husky dog played on it, causing him to leap off in some alarm, and it was so perfect, I suspected the Kulusuk tourist board had set the whole thing up on purpose.

The hotel will organise a boat ride to the nearest glacier, a magical journey through the icebergs, and the pilot will delight in hurtling back at an exhilarating speed, making you feel a bit James Bond as he navigates the sudden twists between the obstacles.

But my favourite iceberg of all was the one that we found in the bright midnight light, which had drifted ashore and had a hole in it custom built for placing a bottle of wine inside to keep chilled. So, we fetched a bottle and had iceberg-chilled wine, content this was almost certainly a level of decadence even Elton John has never managed.

Greenland is extremely proud of its icebergs, to the extent that one East Greenland tourist guide boasts: "It was almost certainly this glacier that produced the iceberg that sank the Titanic." Because they don't just make icebergs, they make celebrity icebergs.

The settlement of Kulusuk contains 300 people who live in huts randomly dotted near the sea. But what's fascinating isn't its size, it's the remoteness. There are no roads out of any Greenland town, they just stop, at one end with icy sea and at the other with mountains leading to glaciers and pre-nailed-up polar bears.

The 300, and you will meet most of them, are excessively sociable. The kids want you to play football, the toddlers want to show you how to clamber over icebergs, and the women puff on their pipes and smile. We were there on the night of the World Cup Final, and Elysa, who spoke English, came running up to say she was disappointed because she'd supported Holland, adding: "But never mind, today was still a good day because we caught a seal and many mussels."

Outside almost every hut is a line of huskies, and sometimes husky puppies, the main method of transport outside the summer, who exude a charm and sense of reliability Virgin Trains couldn't dream of. And there was a shop, which I wasn't expecting, that sold chewing gum, washing powder, and rifles.

After two days in Kulusuk we took a helicopter to Tasiilaq, a majestic chug over the half-frozen landscape, and when it lands even someone who's queasy about flying wants to ask the pilot whether he could go round again. And the Hotel Ammassalik, at the top of the almost vertical Tasiilaq hill, would be delightfully jocular if it was transported to Rome or Barcelona, but because it's in Tasiilaq you nibble your herring while staring with awe at the fjord, icebergs, and mountains, the only place where the reality looks more magnificent than the cover of the brochure.

After Kulusuk, Tasiilaq, with its population of 1,800, can seem a bit of a rat race. It has two shops, and a post office, and a place that sells ice cream, and a policeman, and a football pitch. But, meandering around, we made the most stupendously wonderful unlikely discovery in the history of travel. On a notice board was a sign, written in crayon: "3.00 pm today – come and play cricket."

It seems some Essex schoolgirls were on a hiking expedition and one of them had brought a bat and some stumps. So, at 3pm we played cricket with seven Inuit kids, who had an alarmingly astute sense of timing, and it was such a magical afternoon that if I had any sense of business I'd buy the rights to Greenland cricket and Rupert Murdoch would end up furious at how he hadn't spotted it himself.

Almost as exquisitely romantic are the unfeasibly tranquil lakes in the Valley of the Flowers that would be impossible to walk by without wanting to hold hands with whoever you were with, even if it was President Ahmadinejad of Iran. They entice you in, those lakes, such is their seductive quality, until you shout: "Aaaaagh, it's freezing! Who'd have thought a lake would be cold in Greenland?"

There's also a bar in Tasiilaq, called Bar, where they play Johnny Cash, and Inuit women sit in the corner and smoke pipes, and there's a lopsided photo on the wall of the landlord's 10-year-old son smoking a cigar, and through the window an iceberg drifts by, and outside there's a lamppost that's actually an alarm that goes off before a hurricane, and it's all utterly idyllic.

But mostly, everything you do there, even the most mundane act, is a joy because of where you are. You're not just going to the toilet, you're going to the toilet in Greenland. You're getting bitten by mosquitoes in Greenland. When we had an argument about something or other I thought: "Fantastic, we've had a row in Greenland."

So you must go. And to East Greenland, not common touristy easyJet West Greenland, where everyone goes. Discover the World will sort it out. But don't all go at once – about three of you a year is enough, so as not to spoil the sense of "What you going there for?" And strangely it was warm for the whole trip, even quite hot at times, and we all came back a slightly peculiar shade of brown.

Compact Facts

How to get there

Discover the World (01737 218800; discover-the-world.co.uk) offers four nights in East Greenland from £981 per person, based on two sharing, including return international flights via Reykjavik in Iceland, and air transfers in Greenland, B&B accommodation in Iceland and full board in Greenland. Departures from May to September.