If snow was going to hurt anything on the Teryx or any atv for that matter I don't think they would be selling them. No snow isn't going to hurt your belt or anything on your Teryx. Snow shouldn't even come close to touching your belt.
I would say if you could stay above the snow and still get traction you would be ok. But if it gets to the point that you are riding above the snow and isn't getting traction I would say your going to have fun getting it unstuck!!!