My horse got something that looks similar but on his nose... The skin cracked and peeled and he lost all the hair. It started out as an allergy and then sun made it worse, resulting in chronic dermatitis. We have to keep it constantly covered and zinced. We treated it with a cream that was antibiotic, insect repellant and sunscreen, and now just keep it covered.
Just a thought.
Also it could be something related to/similar to greasy heel?