My horse will cough about 4 times after making a run. He only does this in the arena, when he is running in the pasture or breezing and long trotting which is a lot more exercise than making a run, he doesn't cough. I ran him just recently in a big outdoor arena that was not dusty at all and he coughed several times. I know he has some seasonal allergies, but could he be a bleeder if he only coughs after running barrels, and not in the field?