We have camped in the snow in the Sierra:

But it was not that cold, really -- only about 20 degrees at night. It was colder when we were in Yellowstone -- it got down to 15 degrees outside, and below 30 in the trailer -- the cord on the coffeemaker froze -- this is not a trick shot:

And both of those shots were taken in our poorly insulated first trailer. Our current Fun Finder is a lot better for winter camping.
If you are looking for a winter camping site, make sure that they will plow the road if it snows while you are camping -- otherwise, it can be tricky getting out. Please don't ask me how I learned this -- we escaped, but just barely, when we had a surprise storm.
What kind of a trailer are you getting?