Good pasture maintenance is the most important step in reducing parasites in horses. Parasite eggs, having been dropped in the horse's manure, are then eaten by the horse, along with the grass that it graze nearby. That's why it is important to keep your pastures clear of old manure. Allow your pastures to rest if possible, as many parasite eggs will live for only a short while and rotating pastures helps give time for the eggs to dry out and die. Keep stalls clean and dry as well.
Fly sprays may help repel bot flies and many people pull or scrape the small yellow eggs off of their horse's hair coat so the horse does not ingest them. Bot eggs are ingested when the horse bites or licks at their coat. The saliva loosens the egg, and the egg travels into the horse's stomach where it hatches and turns into a larva.
It is also important to deworm any new horse that comes on the property before you turn it out on pasture. This way, you're avoiding introducing any new parasites to your pastures.