In the winter a horse uses a lot of what it gets from its food to grow hair and produce body heat. Feed your horse hay that is of good quality and pelleted feed. Horses have a harder time processing whole grains by not getting what they need from it. Feed your horse a really good pelleted feed.
Riding in the snow is ok if there is no ice. If there is slushy snow then there is ice. It does depend on what kind of terrain you have below the snow.