I noticed yesterday one horse has a kind of dry irritated cough. No mucous, runny nose/eyes, fever or any other symptoms. He coughs coming out of his stall in the morning to his pasture, and then doesn't cough at all throughout the day. If he had other symptoms I would be taking him to the vet, but that isn't the case.
My horse had this for about a month this summer...vet gave me some cough syrup to give once or twice a day (I think it was actually human cough syrup - smelled and tasted like it at least!) and I kept him away from as much dust as possible (watered the arena, kept him away from the dusty warm up pens at barrel races) and soaked his hay for a while.
It took about a month or so to completely get cleared up! After that I was sure to keep him in as little dust as possible.