MuswellhillDad, my first thought was that somewhere like Flaine might work for you - it's only 1.25 hours from Geneva airport, so ideal for a long weekend skiing and it has an inexpensive hotel. When I went on-line to try to find the name of the hotel I found this operation - they do 4 day and 5 day trips, and prices include accommodation, all meals, ski equipment, instruction and lift passes (so you'd need to add flights and car hire on top). But they don't start their trips until after Christmas. They do a 4 day trip for £379 from 28 Dec, so if being away over New Year is an option it might work?
I have no idea what the company are like though - it sounds like a youth hostel style holiday (but with private rooms as an option). They get good reviews on the basis of value for money on Trip Advisor.
The hotel I've stayed in in Flaine is called the Aujon and is run by MMV, but I can't get their website to work for me at the moment.
Wherever you go, I'd suggest you check when the resorts lift system opens! I think quite a few resorts don't open their lift systems until mid-December.
Resorts like Tignes which have a glacier will have lifts open and will have snow, but Tignes is much further (3 hours?) from the airport so not so ideal for a long weekend.
Ski holiday by coach are usually much cheaper - ski weekends have [http://www.skiweekends.com/pages/skiweekends/search.aspx?searchBoxCategoryId=31&pdDeparturePointId=8&startDate=6%2F12%2F2013&searchWindowSizeInDays=2&minNights=2&maxNights=9&paxCount=2¤cyId=1&searchType=Webookit_Direct&pdResortId=1|14|17|23|24|26|35&autosearch=true this]] trip departing 6 Dec for 4 nights, 3 days skiing for £199 (incl. travel, accomm and half-board).
Hope that's of some help. Good luck with finding your ski hol!