Christmas is pretty early on in the skiing season and you can be very lucky and have great snow cover by then, or things could go the other way. If you wait until November to book you will know at that stage what resorts are getting a good start. I believe the brochures only start their ski holidays on the first travel date that will include Christmas Day in the week, probably because there have been some years that many resorts were still green well into December.
You will read much about how many snow-making machines a resort has, but it doesn't matter a damn if the temperature is too high for them to work! Given that Christmas week is so expensive for skiing (& New Years even more), it would be awful to end up somewhere without decent snow cover, especially for your first ski holiday.
Here's an article from 2001 that illustrates what happens when the snow is late. Christmas snow in [broken link removed] was very thin on the ground, it was into January before things improved. However, the last 2 years have been very good.
But if you must book this early in the year I would recommend going as high as you can, probably on a glacier. Or you could book somewhere like Norway but I believe it's very expensive, and bound to be even more so at Christmas.
Austria is supposed to be great place to go for Christmas atmosphere. Should you go to France be warned that apartment sizes are tiny.
A good resource for ski information is
www.wtss.co.uk