Clip the legs. I would put boots on when ridden to protect the legs from direct contact with mud, snow, dirt, and ice.
Towel the legs dry after riding or use a hair dryer and stall in dry shavings.
Another option is pymethrin shampoo, but that only works if your horse has skin mites. My mare picks up mites when riding during the summer and breaks out in oozing sores. I doubt that is contributing in your case, as you are in snow.
Wet is the enemy here. Bacteria and fungi take up residence in those sores making them difficult to heal. I would try triple antibiotic ointment with clotrimazole ointment.