it would be pretty poor with snowshoes I think, the problem is you get some complex layers even on flatter ground and you tend to crash through them, invariably the shoe dives forward and you’re stuck in place.
Here’s some bozo who’s just done exactly that fortunately captured by an amused bystander on camera:
just about to dig himself out ..
in answer to where’s good… anywhere really, by early June you’re expecting below 2000m to be mostly OK but you’re going to want to avoid exposure to steeper slopes above if they’re still holding snow. I was in the Vanoise a few weeks back and it was pretty great, some of those huts will be open in June. You’d not generally expect to do the glacier tour until a couple of weeks later but it might go.
Or, take a bike and try the Jura, entirely snow free and pretty good mountain biking. All the pre-alpes is pretty much snow free now and will be nearly totally by mid-June.
Or.. grab a cheap flight to somewhere else, Morocco will be fantastic, not too warm yet, I’m thinking of Crete or Sardinia personally but Kosovo looks interesting. Corsica would be good but even the GR20 is likely to have snow until late June.