My big eventer gets a horrible cough when he eats hay or is in a dusty environment. You can try feeding Haylage instead of hay, steaming you're hay and make sure if you're horse is in a stable to have it well ventilated! :) if your horse is still coughing it could be a good idea to get him scoped at the vets. :)
I was always told if a horse coughs and then clears his nose afterward, so sort of snorts, then it's fine but if it coughs without snorting you should get the vet to check them
You should get it checked just in case if it happens often.
If you're worried try and eliminate possible causes one common cause i come a cross is dust and if you live in a particularly dry climate, I suggest lightly soaking the horses hay with water... (if it is a dust related cough.) hope this helps :)
My horse tends to cough every once in a while. It's usually not an issue, but if you notice your horse is coughing often, I would get it checked out 😊