Manure piles attract flies. Try beneficial insects to control flies around your stable area. Forum members have experimented with beneficial insects with mixed results.
Clear manure away from paddocks frequently.
Clean stalls frequently. Manure and urine that is left to sit will attract flies. The odor can become unpleasant and ammonia build up can adversely affect air quality in your stable.
Try homemade fly control sprays on your horses. Some people swear by them, although some of them don't seem to work well for very long. Luckily most homemade recipes are cheap to mix up.
Keep your horse on a regular de-worming schedule. Ask your vet about suitable organic alternatives to parasite control and whether these are recommended for use in your specific situation.
For rats and mice consider keeping a barn cat or two. Humane traps can take care of other unwanted critters in your barn.
Try Bti pucks or granules in ponds and areas of standing water for mosquito control.
Muscovy ducks can help control flies in the barn. They are also will catch mice, believe it or not.