Is this just $2000/EUR per month for rent + utilities or is that budget including all basics, like food and skiing?
USA/Canada you could get a lot lower of a price.
Gudauri resort in Georgia is amazing too, and far, far cheaper.... $12/day to ski about probably the cheapest price anywhere. Incredible skiing.
Also some very good places in Andorra and nearby in Spanish Pyrenees.
I am interested but can't join until January, will be skiing/visiting family in Montana, USA which also is remarkable... look into Whitefish ski resort or Big Sky!