Alright first off I am going to say that riding in the snow is fun and for the most part is just fine. However if the snow is too deep it can get a little tricky and you can easily push a horse to hard in it. I say this only from my own experiences. Usually if it is too deep the horse will start getting stuck or laying down. Most lay down, (not on their side but straight down). If you have one that will give you their best be careful, my mare who will do whatever I tell her was pushing snow with her chest going down a hill. Then she jumped into a drift. Well needless to say she disappeared under me ( it was that deep). The bad thing though when she tried to get out she fell on her side and I had to dig her out. Bad thing the way she was positioned she was suffocating. I dug fast and got her out okay but since then I try to be a little more careful.
Another experience with a mare that give you all her heart she was sweating really bad all over and the white foam was rolling off of her. Well not much after that she started coughing up blood and kept trying to lay down. I know I shouldn't have pushed her that hard, but I didn't know I could hurt her and I was younger at the time. I guess we learn the hard way sometimes, because after that I packed the saddle the 2 miles back home on my back and once I got her up and a little rested. Sadly after that she was never the same and could no longer handle very long of rides.
So I would say yes ride, but do be careful. My rules are if it looks to deep that they might get stuck don't go in and if the white foam starts let them rest.