Like others from Alberta, I also ride in the snow. If we didn't, we wouldn't ride for nearly 6 months of the year. That said, I do love riding in then snow, especially bareback. The horses seem to enjoy it too.
As others have mentioned, you do have to know what the footing is like. Snowdrifts can be surprisingly deep, and ice under a layer of snow is very slippery. Also, watch for the crust on the snow. I've ridden in conditions where the crust was so hard and sharp, it can cause minor abrasions on the horses legs. The snow balls up in their feet if is wet. We simply clean out the horses hooves before and after. I also use a bit warmer, or ride in a bitless bridle in winter. Horses do tend to sweat much more in winter due to their thick winter coats. We either use a fleece cooler to help them dry and keep them warm, or blow dry them before turning the horses out again after riding. I also don't ride when it is really cold ( below -20 Celsius). Not only is it uncomfortable for me, but I also worry about the horse working hard and bringing cold air into their lungs.
Riding in the snow is a great way to keep you and your horse fit over the winter. Riding bareback and bridle less also help develop the riders seat and the horses response to more subtle aids.