I ride 12 months of the year. So I do ride in snow. We try to avoid the really deep stuff. Ride on the West and South facing hillsides. The North and East slopes get much deeper snow because it doesn't melt off as fast. I also avoid heavily used trails that hikers and cross country skiers use. They pack the snow down to much and create ice that the horses can slip on. I don't worry to much about sliping on snow. But ice is definitely something to be avoided, Especially if you leave your horses shod during the winter.
As mentioned above, I try to avoid areas with heavy crust. It abraids the horses legs.
One of the beauties of riding in the winter is that I can see more wildlife. They are forced by the snow to congregate. The leaves are gone, so they area easy to spot.
We try really hard to not harass the wildlife. They don't need the added stress during the winter months.
We ride a lot in the desert during the winter, mainly to avoid the really deep snow. One of the advantage of where I live is that I have easy access to both mountains for summer rides and desert for winter riding.
I leave my horses barefoot for the winter months. Hence no snowballs under their feet.
We carry food and firemaking materials. When you are 2-3 hours from you truck, You are responsible for yourself and your animals. We've had horses go down in streams in the winter gettting the riders totally wet. So I usually carry some white gas, or other flamable to quickly start a fire if neccessary. Besides it more fun to have a hot lunch on a day ride.
I haven't really added much to whats been said about deep snow. I guess my comments lean more towards, Go out and have fun and enjoy it.