Good luck with that! If you find a snow-sure, ski-in/ski-out chalet with maid service and spa facilities in a pretty town with lots to do for Christmas week ANYWHERE for less than 5k, keep quiet about it and guard your secret with your life. I’ve been looking for something similar for years and they are hard to find for double that budget.
There a few things you could try to achieve your dream. You could up the budget massively, or relocate your ambitions, or downgrade your list of requirements.
You could find a pretty chalet in a smaller town with fewer activities but decent skiing for that price, or a winter wonderland with very limited skiing, or if you look very hard and are very lucky you might find a winter wonderland with skiing but you might have to ditch the maid and spa.
Look at the Scandi places - they are not well-favoured by skiers as the skiing is not extensive, but what skiing there is is beautiful, and there are lots of other activities like husky mushing, snow mobiling, and naked outdoor sauna-ing! It is dark though.
If you say sod it and up the budget, I would go with a package company. Scott Dunns will find you that Wham video dream, at a lottery win price, but Crystal or Neilson will find you a Christmas week in a ski resort somewhere for your set budget (maybe!)
The final thing to consider, if your budget is definitely set and you want to make the most of it is to wait till the start of December and hoover up a cancellation at bargain price, as most people have their Christmas plans locked in by then. Takes nerves of steel to hunt and nail down this approach though.