Note that you need different control strategies for different kinds of "bugs". Mosquitoes, stableflies, horseflies, greenheads, gnats.... each has its own DIFFERENT place it breeds and DIFFERENT rules of engagement regarding time of day, shade/sun, repellants, part of horse afffected, etcetera.
So other than putting flymasks and turnout-type fly sheets on, beyond that you need to look at what KIND of flies the problem are, before you can intelligently figure out what to do about them.
BTW to the above posters' lists of "all the things that you can do that sometimes help with some fly situations" I would add providing a fan or a windy place to stand, and in some cases (NOT for mosquitoes, which appear to be part of hte o.p's problem) turning out at night instead of daytime)
Unfortunately the only things I know of that really help for mosquitos, and even that is far from satisfactory results if you have a bad skeeter problem, is a) apply waterbased citronella-type repellant (e.g. Bronco) heavily at dusk every day, b) have horses wear all available fly masks/sheets/wraps, c) stall them at night in a barn that is either FULLY mosquito-screened or have a safely-rigged fan blowing in each horse's stall. People always say "drain all standing water" but honestly I have yet to EVER see a place with serious mosquito problems where most of the skeeters were bred *on* the property... mostly they are from elsewhere, if you gots a lot of 'em.
Pat