Eurail covers all the countries you plan to visit except Britain, so you don’t need to worry about places that Eurail covers.

While there are plenty of ski centres dotting practically every mountain range in Europe, particularly the Alps, where you will be near most of the time, it won’t be hard to find a place to snowboard.

One thing that I recommend, and everyone will agree with me on this, is to skip Geneva, and instead stay in Bern or Thun, lovely cities. And there’s plenty ski places near those towns, that are just an hour or maybe 2 hours away. (I found this list of places near Bern). You can do the same by skipping Vienna in favour of Salzburg or Innsbruck in Austria.