I live in Fairbanks, Alaska. We have extreme cold and a lot of snow some years. I brought my stallion up from Alberta, He is 15 hands. We have two other quarter horses of the same size and a mix, also of that size.
Honestly, if you have a designated paddock or pasture that you keep your horse(s) in the whole winter, the snow should not be a huge problem for the horse. The horses pack down their regular used areas really well. I once boarded at a place with a shetland and a miniature horse who also did just fine in the snow. I even ride actively in the winter - I just ride the same trail and in the same arena to keep it packed down well.
The hardest part about a lot of snow is feeding, moving hay, and cleaning manure. Try to figure out a system for all of this to make your life easier before the snow flies. :)