Some horses will get itchy skin if the sweat/dander isn't cleaned off them.
Cleaning them up after drying them off from a workout should be part of the time spent with them.
After using anyone of the drying off processes already mentioned, give the coat a vigorous cleaning with a metal shedder to get the dander up then vacuum the horse.
I vacuum all my horses during the cold months --- with the shop vac. Just be sure to use a brush attachment because a brushless attachment sucks their skin up and most horses won't appreciate that. I have one out of four that thinks that's fun on his shoulders and but