The big differences between Mountain bike goggles and Snow goggles are the following.
1) MTB goggles typically have a single walled clear lens (and can have tear off lenses for riding in the rain/ mud).
2) Ski goggle lens may be two walled to help keep goggles from fogging.
3) MTB goggles are typically cheaper because the lens quality is cheaper, and less to replace.
4) Ski goggle lens are usually more expensive because the lenses are usually better optically for dealing with various snow / sunny conditions.
5) There are a few ski goggles that are very large, and might not fit easily into a full-face mtb helmet.
Some of the best ski goggle lenses are made from Oakley with the Prizm lens that comes on the Oakley Flight Deck XM Snow Goggles which are worn by the world's #1 ski racer in the world Mikaela Shiffrin. The Oakley E-Frame goggles are less expensive double walled ski goggles, that can also fit easily into a full face helmet for mountain biking.
Popular MTB goggles that don't cost too much are the 100% Goggles.
If you're planning to wear your goggles over a full-face mountain bike helmet, then certain MTB goggles will fit better over a big helmet. In this case check out the following goggles: Oakley Airbrake MX Goggle or 100% Racecraft Goggle