Norway, as suggested higher up is not a bad idea. Plus your near the Arctic, so presents an extra snow like twist.
If you’re not wanting to ski…then I’d try skiing. Bear with me. I mean cross country ski ing. Avoids all the faff and the Timothy and Imelda’s and the resorts. For this, Norway is great, but I’ll stick my 2p in and suggest the Jura. Immediatley north of Geneva along the border of France and Switzerland. Easy access. It would even be worhtwhile for a long weekend. Have a play on the planks. Hire kit is dead cheap and dead easy to arrange.Signposted prepared trails, Then you can go sledging, snow shoeing, sittng in nice local not ski set cafe’s, visitng Comte (the local cheese) factories etc etc.
For accommadtion there are loads of great value gites which offer half board and are very family orientted dishing u plocal food etc. None of this generic pizza in a concrete jungle on top of a mountain rubbish.
Contact me if you want further details. We live about an hor away from the Jura.