If I keep the stable dark and ideally cool as well, the horse flies turns around at the door here. They are such large insects, and need to keep that large body heated enough, so they stay in the sun. I have one stable with regular boxes for the horses, and one stable where the horses can walk freely in and out. During daytime the horses refuse to go out by free will, and they stay as deep as possible in the shade of the stable. I can literally see the horse flies smell the horses but they turn around when they enter the shade just inside the open door.
As for keeping horses the "natural" way, I agree with the comment Macaroon made. There is nothing natural about keeping horses fenced in and on top of it all deny them shelter. In nature animals that are troubled by insects have various alternatives to reduce the pressure from the flying beasts, like moving to higher and open grounds with more wind, mud baths etc. When we take things like this away, we really should give them another option.
