>>450218It's all snow over 800m and all met cold and mud below 800, so you either go ski or snowshoe touring. Given the current snow situation ski touring is highly dangerous, avalanche risk is severe.
If you go skitouring you need a guide, equipment and at least 4 people in the rope team. also you'd need reservations/keys for the high mountain huts which are normally closed. Some dieharders might bivouac but this needs more and expensive gear to carry and really good knowledge. If you want to go touring, book a guided one, theres plenty on the internet.
Snowshoeing is a bit easier as long as you stay below timber line. I'd still recommend to team up with someone and check for huts first.
The Hohgant tour is a nice snowshoe overnighter trough oldgrown mountain forest close to Interlaken. You can spend the night at Hogahnt hut, it is closed at winter but you can get the keys.
Another option would be to go winter touring in the Jura region around Saignelégier (etang de gruère), a thinly settled mountain plate around 1000m above sea. You can go there snowshoe walking for days, light forest, fields, rolling hills.
Greina Valley is pristine and remote, this would make a nice 3-4 night alpine snowshoe tour, but you will need a partner and full winter gear.
Switzerland has Jedersmannsrecht (freedom to roam) so you can camp for a night or two at the same spot, keep out of sightline from buildings, don't camp in a national park or game reserve, do not cut down living trees. It is good custom to leave after a night or max two nights and leave as few traces as possible. Winter camping is pretty hard and especially above tree line it is also dangerous.
With the latest events at the currency market Switzerland is likely one of the most expensive countries in the world. In case you go shopping, Denner is cheapest, Migros is best for the value.