I use to have a similar thing with a stud colt of mine. 1st is he kept in a barn? It could be allergies, I know I sound ignorant but it's true. If people at your barn blow it out with a blower or sweep it out or use dusty shavings/straw that could be a possibility. My colt had the EXACT same symptoms.
Or, COPD, heaves, pnemonia, and choke are my next ideas.
Bring your horse up to a canter and watch his flanks when he is in motion. If they seem to lift twice per stride that could be an indicator of heaves.
Choke is unlikley as it sounds as though it's not just during mealtimes but also provoked by exercise. Try wetting his hay and feed though. This will also help with any type of respiratory issue!
Pnemonia is another likley cause due to the sudden changes in temp and weather. They seem to go down in the summer for whatever reason. What's his temp?
Good luck with your horse! I'd love to hear more and find out what your vet has to say.