Consider Chamonix
LC – Yes, of course you could drive to Baqueira and ski with the same people you meet and work with in Madrid. Or for something smaller and less-Mercedes and more-Peugeot, to Cerler. But if you want Alpine and quaint, may I suggest Chamonix? Lovely town, good skiing (both cross-country and downhill), good food, and some cozy inns where you can enjoy a glass of late-night Armagnac.
I haven’t been there in some time, but it did not seem to me like the kind of place that would change easily. I believe there is even a bus from GVA, if you don’t want to rent a car.
And if you insist on the “cabin in the forest” ambiance, rather than “small hotel in town,” AirBnB has a page of about 30 chalets listed.
Bon voyage!