Not all of us are fearless, Amazonian types who relish the prospect of hurling ourselves headlong down steep slopes. But we do want to experience the mountains and snow, the scenery and the celebrated aprés-ski, even if it is just from the safety of the valley.

So which are the best resorts for the nonskier? Where should we take our ski-shy partners, friends and relatives? And how can they keep themselves amused while we dash off to the slopes for several hours each day?

Switzerland is particularly good for off-piste entertainment. Davos, Klosters, Gstaad and the especially glitzy resort of St Moritz specialise in a host of novel wintry pursuits to divert the reluctant skier. St Moritz is beside a lake that freezes over to become a giant playground for all sorts of activities, from golf (played with red balls), ice hockey and polo, to horse racing. There is also top-class shopping in its dreamy designer boutiques.

Davos, similarly, boasts excellent spectator sport facilities for speed skating and hockey and has the biggest natural ice rink in Europe, while Gstaad has a good tennis centre and pool complex.

Cortina d’Ampezzo, in the Italian Dolomites, is a haven for shoppers, stuffed full of upmarket emporiums and fur-coated Romans and Milanese more interested in showing off their latest fashions than their fancy ski manoeuvres. Long lunches are popular here and there are many fine pizzerias and trattorias in which to hang out. An added advantage is that Venice is just a couple of hours away.

In Austria the best resorts to head for are Zell am See, Kitzbühel and Innsbruck. Zell is, like St Moritz, a lake-side resort, just a handy day trip away from Salzburg. Nonskiers can go on magical walks across the lake or visit an excellent motor museum. At Innsbruck there is a museum dedicated to the Olympics – it has hosted the winter games twice – and a zoo.

Despite being a mecca for the serious skier, Chamonix in France is also good for more reluctant ones. There are great shops, superb hiking trails, a worthwhile, if small, Alpine museum in the town centre plus possibilities of excursions to Geneva and Annecy, as well as Courmayeur and Turin in Italy through the Mont Blanc Tunnel.

Courchevel is another good option for the can’t ski, won’t ski brigade. About 30 per cent of the resort’s visitors have no intention of skiing or snowboarding, so a whole industry has grown up, offering everything from driving Porsches on ice to loafing about in fur coats.

Most resorts, however, will offer any number of alternative slope-side activities, from trying out dog sleds, snow shoes or snow mobiles. Visitors need only ask at the tourist office.

For the outright refuseniks there are the spas. Many of the smarter hotels in the classier resorts offer spa facilities. Austria has an excellent range. Bad Gastein, near Salzburg, is a world-renowned spa town with thermal waters, while Kitzbühel has old-school glamour, classy hotels and spas to match. Grindelwald in Switzerland is a great spa weekend destination.

Or you can visit Whistler in Canada, stay at the Fairmont Château and be pampered to your heart’s content.

Alternatively, you could just go star spotting in Aspen, Colorado, or curl up in your chalet with a good book and a mug of hot chocolate in front of the fire, something of which I am always envious when being dragged up the slopes in sub-zero temperatures.

A day at the race in St Moritz is pure white magic

One of the most thrilling spectacles in the Alps is White Turf – a series of racing days held in St Moritz each February, when horses run on a frozen lake.

The event is the resort’s biggest annual attraction, drawing thoroughbreds and more than 30,000 visitors from around the world. It is an extraordinary sight to behold, even for nonhorsey types.

“It is just fantastic,” says Barbara Keller, director of international relations at White Turf, sipping on a glass of champagne beside the track. “Even if you know nothing about horses or trainers or betting, it is an incredible event to see.”

Racing takes place on Sundays in February and each race day consists of a number of events, including flat racing, trotting and skikjoring, in which jockeys attempt to stay upright on skis and are pulled along by the horses at terrifying speeds of up to 31mph (50kph).

The horses wear special shoes to stop them sliding around on the ice and they do not seem to be alarmed by the unusual surface.

There is no fear of the ice breaking because it is between 40cm (15in) and 80cm thick and capable of withstanding 29,000 tonnes of weight, which is just as well, given that each meeting has to support about 10,000 people, 75 tents, 1,000-plus cars, chandeliers and countless bottles of Krug champagne.

White Turf takes place on February 3, 10 and 17 in 2008; www.whiteturf.ch