If one wanted to buy a place in the mountains where you can ski in winter and hike in the summer. Are there any nice places to shortlist where you can get a modest place which doesn’t break the bank?
I’d also consider off-grid huts. Looking in Switzerland and maybe neighbouring countries.
By “get” you mean rent (short/long term) or buy?
In Switzerland only or neighboring Alps as well?
updated to say “buy” and CH and surrounding countries.
Depending on how small a ski area you are willing to get access to, I’d recommend “La Fouly”, in Valais/Wallis, as a very nice place, with a tiny ski domain but very nice hikes to do in the summer. Probably nicer if you’re also into ski touring and not only after official ski areas.
There are probably plenty of places like that. It’s just the one near me that I’d consider living in.
I´d consider Ovronnaz
On French side at less than 2h drive, you also have Praz-sur-Arly and Espace Diamant.
Aim at February and March as snow is not always guaranteed.
What about on the German side ? Any recommendations
which German side? There are no skiable mountains in south germany, close to us.
Feldberg would be the biggest area. When they have good snow once in a while the area is packed with people.
Please don’t reveal the good spot in Wallis 
Good others spots at decent price in among many others: La Fouly, Ovronnaz, Nax. Moosalp und Lauchenalp in Oberwallis.
Never been, but heard about Oberstdorf:
indeed, looks like there are some mountains in south germany. Obviously my thoughts stopped at lake constance
Meant Swiss German side 
GR or Engadin cantons
I think the Val d’Hérens (Evolène, arolla) is exactly what you want.
Pretty villages with beautiful old chalet and wooden houses, beautiful views, sunny, easy to reach and affordable housing (but not a lot) around 6k/m2
Ski resorts are small but sufficient and will grow (projects ongoing)
How high do you think this would need to be? I think altitude should also be a consideration.
We were in Chamonix at 2500m last week and while there is plenty of snow it is nothing like 5-8 years ago and surely nothing like 15 years ago. My main concern would be whether or not there will be snow wherever you look.
I taught my son to ski at Les Paccots 10 years ago and for the last 2 years there is hardly any snow there