MARK the reindeer was having a few days off work to get his head together. He'd just shed his antlers, so our reindeer for the day was Will. We'd come to Kikut, high in the mountains above the Norwegian ski resort of Geilo, to find out a bit more about the animals.

They are smaller than you would expect from the conventional pictures of their seasonal work with Santa Claus. They're goat-sized and barrel-shaped, with thin legs and large feet - perfectly designed for a landscape where the snow begins to fall in September and doesn't melt until May.

Harald is a reindeer expert. He runs the Kikut reindeer centre with his son Ian, whose grandfather left his job on the railways in Darlington to move to Norway. We left Mark searching for food in the deep snow and climbed onto the sledge two at a time, then hurtled round the frozen lake behind Will.

Reindeers, though we expect them to be as cute and cuddly as Santa, actually hate people. They loathe being stroked and remain 100 per cent wild animals. But a creature that can survive on anything in any conditions demands respect. For the last 40,000 years they've remained the same, pottering about the Norwegian mountains, dodging wolves.

As we sat defrosting round the fire in the traditional Norwegian hut lined with the skins of Will and Mark's relations, Harald told us about the other occupants of the hills. These included the brown bear that had been recently discovered nearby, far from his normal stamping grounds. He's currently hibernating but his first waking moments of spring are likely to be recorded by a posse of Press photographers rather than hunters.

Wolves are now protected in Norway and live further north. One recently went walkabout and wandered down to southern Norway, a scientist with a tracking device close on its heels. Feeling it probably unwise to mention its presence to local farmers, they kept an eye on it, tranquillised it and sent it back home by helicopter.

We - that's me, my husband and three children - walked back warily out to our taxi and the 21st century.

Last year up here the temperature fell to minus 40 degrees. No wonder Amundsen got to the South Pole first - it must have seemed like a Sunday afternoon stroll to him.

Down in Geilo, they depend on the snow. As one of Norway's top ski resorts, it opens early in the season and closes late.

We were there for the snowballing, but holidaymakers who were there for the skiing said how civilised it was on the slopes, with none of the macho aggression found further south in Europe. Cross-country skiing is also very popular here.

We stayed in the hospitable Highland hotel in the centre of the village. The hotel's facilities for families are excellent with table tennis, computers and Nintendo, as well as traditional drawing materials, all free and readily accessible. There are film shows and a swimming pool, useful at the end of the short winter day.

Before we went to Norway, friends muttered dire warnings about the short hours of daylight. Blink and you'll miss it, they said smugly. Actually, in late December in this part of Norway, the sun rises about 8.45 behind the mountains, creeps along the top of them and sets about half past three in the afternoon. Not a lot different to a British winter's day, though with the brightness of the snow and frequent blue skies, it's a lot more cheerful.

Geilo has plenty to offer the reluctant skier, largely based on the outdoors. We went dog sledding, skimming inches above the ice, behind teams of excited dogs, who are champion racers in their spare time. If you prefer something a little more leisurely, there are also horse-drawn sleigh rides.

The children and their father, who doesn't usually exert himself in such an ungainly manner, went on a two-hour snowboard taster session, and loved it. Weirdest of all, and the biggest hit with the kids, was snowrafting.

Having just recovered from flu, hanging about on a Norwegian hillside in deep snow, in a blizzard, at night, was probably not what the doctor would have recommended. But there I was, queuing up to be pulled around by a snowmobile whilst clinging on to something that looked like a giant inner-tube. Strangely enough it was extremely exhilarating.

Geilo is halfway between Oslo and Bergen on the main railway line that connects the two cities. It's said to be one of the most spectacular railway journeys in the world, passing through high exposed mountains.

We travelled from Oslo to Geilo through miles of snowy forests with little wooden houses in the valleys and occasional towns. Frozen waterfalls and snow flurries passed the window. I've been on boring train journeys and this wasn't one of them.

Oslo took our breath away... well it was 14 degrees under zero when we arrived. It is a serene and unhurried capital, relatively traffic free due to a Ken Livingstone-like set of toll charges on vehicles in the city centre.

We stayed in the wonderfully Edwardian Hotel Bristol. Agatha Christie would have felt happy to leave some of her characters there, taking afternoon tea in the book-lined, plant-filled lounge, as the pianist tinkled on.

Oslo's winter appeal includes its many museums. The artist Munch has one, as does Nansen's boat, the Fram.

The drawbacks, well yes, Norway is expensive. There is no avoiding this. But if you stay half board in a hotel and don't plan on eating or drinking out too much, it is manageable. Supermarket prices are reasonable for snacks for hungry children and the hotels offer hearty breakfasts as standard.

But the incredibly friendly and helpful Norwegian people outweigh any economic consideration. They look much like the British, only a few are blue-eyed blondes. Generally they would not look out of place in the checkout queue at Tesco in Middlesbrough. They'd probably be a bit surprised at British prices but they'd be rushing back home for that wonderful snow.