Yeah. Horses attract biting flies - which can cause all kinds of problems for their riders.
Horse flies and deer flies are between 3/4 and 1 1/4 inches long. Horse flies seldom bite humans, but may accidentally bite riders (they can't always tell where one animal ends and the other begins). Some other biting flies will target humans, but they tend to prefer the blood of large grazers.
Bites are painful and can on rare occasions become infected. Modern riders use insect repellent to try and keep them off. (At a lower tech level, herbal repellents might be used). We also sometimes put a fly mask on a horse (previously mentioned).
Fly predators - a species of wasp that lays its eggs in fly eggs - are sometimes released around barns and can produce a significant reduction.
Flies are more likely to annoy your characters...and their mounts...in wetland areas, or near lakes or rivers.