Does it snow as much? I figured in the mountains it would snow like crazy.
Not in the great majority of places. You can get a lot of snow accumulation in the Carson Range (west part of the state) above 6000 ft or so, and in the Ruby Mountains in the east. I've seen 5 ft or more from a single storm. But not many people live there, except around Lake Tahoe - the mountains are mostly National Forest or state part.
Otherwise, there is not a whole lot of snow - it is a desert, you know. It accumulates in the mountains, but in the valleys, a big snow will typically stay on the ground for a few weeks at most. It's a combination of the low humidity and that larger temperature range - highs will almost always get into the 40s or above, then drop to teens or 20s overnight.