If he only coughs right at the start of a ride, it might be his way of warming up — maybe there was something on the bit that triggers a cough. Maybe the bit itself triggers coughing. You get something in your mouth and it can trigger cough. Horse may have some unswallowed feed/grass/hay in his mouth that suddenly triggered cough. (Horse can hold grass a long time — how many times during worming have you taken him off pasture, kept him out for 1/2 or more, put the tube in his mouth and out comes the wormer with the wad of grass attached). My horse does the same thing right when we start trotting. He has to stop and cough. Then he’s fine. He doesn’t cough while out at pasture. Only at the start of a ride. The pony coughing and passing gas is funny….sorry! Now, if he is coughing while at pasture/rest/stalled, then you may have a problem and the other suggestions per mold/dust/etc should be considered.