I agree with Joan! I have not once picked bot eggs off a horse, and not for lack of trying to find any! I do get the odd face fly swarm, but they are never prevalent.
Don't forget about the black flies, Joan! I hate them, at least you can hear our heliskeeters landing.
Other than hoping flyspray works... the only way to keep them off the horse is manually making sure they are off the horse! Which is a bit of a pain in the butt.