If this is new, evaluate any changes in bedding, stall cleaning practices, ventilation, hay source, and feed. Mold in hay, ammonia in bedding, lack of air moving, seasonal pollen allergy, increased dust in the aisles or stall, or even insect repellant sprayed near your horse’s face and nostrils can trigger coughing. It may be the horse’s reaction to any of these and his way to clear his throat. If it gets worse, or persists for longer periods, have your vet examine him. If it goes away after all the weeds are through pollinating, he may have developed allergies. Most “dust” in hay is really mold spores, which would necessitate changing your hay. Wetting the hay may help, but will not eliminate mold spores, just keeps them from being inhaled as the home eats.