agreed, it's all a matter of luck on actually being snow covered at christmas time, else you'd have to go "up".
but to be sure, a place in the alps doesn't have to be a ski resort. there's lots of towns up there where there's more than just ski lifts.
FYI, over the past few years I've spent christmas at:
* Bad Mitterndorf in Austria (lots of snow above a certain altitude but it's a ski town)
* Kaprun in Austria (not lots of snow, not strictly a ski town, but nearby Zell Am See isn't). Spent the week before in a very snowy Bavaria, but this was after weird snow storms.
* Wells in England (after the freak snow storms, so lucked into LOTS of snow)
rented a house (happily sleeping 4-6) each time for about E1000 for the xmas-NY week.
what kind of budget do you have? particularly, what price, per night, are you willing to pay to sleep everyone?
you could go all out and go to Zermatt, for example, or go budget/adventuresome in somewhere like Slovenia.
oh, and i don't think you're leaving it late... but take too much longer to book something.
