Yes, take a Ryanair flight to Norway. The tourist club (turistforeningen.no) has cabins all over Norway for about £10/night. They are all close enough to ski to the next one. It's a fantastic experience.

Hi Spadge

Where can you fly from? Do you want to hire a car? Are you looking for winter sports if so do you already ski or are you wanting to take lessons? Ryanair have some cheap flights to Salzburg. They also have flights to Munich, Friedrichshafen and Memmingen in Southern Germany, you would then be very close to many resorts in Austria, Germany and even Switzerland. Easyjet also fly to Munich, though both Austria and Switzerland are not exactly cheap. For ski resorts Bulgaria seems to be the cheapest right now. If you have only four days you will probably won't want to travel far after arriving at your flight destination.
December is always a bit tricky for snow in the Alps, some years there's loads other years it doesn't arrive until the new year. There is already snow on the high mountains but the resorts and valleys are pretty bare and the last couple of weeks the weather has been pretty mild.
Give us a bit more of an idea of what you want to do and maybe some more members will have some advice.

Judith

Not sure if I'm too late, but I've noticed that there are some big offers on snow holidays on line with Thomson Ski and Crystal