I have been though all sorts of coughing with many of my horses and was explained by the university of Montreal equine section that no coughing in horses is normal. Coughing is caused by inflammation in the lungs that can be irritated due to an allergy or irritant. During the colder weather horses often have more exposure to dust which is a big problem. My imported mate is very sensitive and requires all hay to be fed wet or steamed and this has made all the difference!!!! Even on meal with dust in the hat can cause her to cough for days but only when ridden.
Has he seen a vet? Maybe that's because of the weather, maybe an allergy or an irritation because of the dust... If you want to hep him, I recommend you to give him an infusion of thym and honey and put it on the food, it helps a lot to me, I give them sometimes during winter :)