A pitchfork, some elbow grease, and a large piece of geotextile fabric.
Fastidious, fanatical manure control--removing poop from all areas near the horses daily at least, and keeping the pile covered with dark fabric that will deter fly reproduction while speeding composting. It's chemical-free, environmentally friendly, effective, and FREE!
There are plenty of ways of making fly traps out of milk jugs or soda bottles and something stinky to attract flies. It won't work on all species, but it can help with some. Sticky traps work well for biting flies, and I would think there are ways of making home-made glue for traps.
Horsefly and bomber traps can also be built from scrap materials--do a search.
It pays to know thine enemy. Figure out precisely what type of flies are most prevalent, do a little research, and you can figure out what types of traps or deterrents work best. Then applly some ingenuity and you might just build a better fly trap!
The only fly control I've ever done has been fly predators and keeping the paddocks picked and the pastures dragged. About $30/mo for the fly predators. I put them in the main manure pile and also in a couple other damp areas near the barn. They do a *really* good job here. I also keep the dry lot picked out or at the very least dragged so the manure breaks up and dries out so there's nowhere for the flies to lay eggs. I drag the fields a couple times a month as well, again so the manure dries out and there's nowhere for the flies to lay eggs.
I don't cover my manure pile or do anything to it except add the fly predators once a month, but it is in direct sunlight.
Yes, I use predators, too, and a feed-through fly control (Solitude) which both help. For years I thought the predators were a waste but this year I gave them another chance and was pleased with the dearth of flies.