Just guessing here but to me it looks like a contact dermatitis of some sort. Check your fields for plants, bushes, or trees that could create a striated pattern (as shown on your horse) from the horse rubbing up against it or walking/running past it. Kind of like a person who gets red lines that show up after scratching themselves. My sister scratches her arm for example and the scratch line turns red and puffy. I agree that an oral steroid may help. If your vet orders it, horse takes it, and skin problem disappears..you have your answer! But again..just a guess. Good luck.