Brushing. Lots of brushing. The air kills the fungus which prefers a stuffier home.
Blanketing isn't a bad idea, Anon. I've heard of baby oil being used to smother the fungus. Mostly I just pull off the scabs once it's broken through the hairs. Exposure to open air seems to kill it, so aggressive brushing should keep it from spreading too much.
Assuming you have a run-in shed for your mare to get out of the rain if she feels like it. On the other hoof, many don't so … yeah.