From my experiences with horses coughing, it has been an alergy, to the hay dust. When I bought a better quality of hay, the coughing and the sinus drainage stopped. I live in an area where the lowlands flood during the winter. During haying season, the hay is cut close to the ground and it picks up the silt left by the flooding in the winter. Thus, dusty hay. I buy in the valley now, and there has been no coughing.
it all depends how many horses you have, and how much work you want to put in them, but if you have the time, soak the hay in a barrel of water for a few hours, then let it drip out in a net, or a barrel with holes in it. the dust will be gone and hopefully your problem will be solved.
If your horses are in a stable, and you're having a very moist winter, this may also be the problem. make sure your stables are dry at all times, moist air gives them what we call "stable cough" in Belgium. I have the same problem every year with one of my mares. Talk to your vet for some respiratory powder. (usally white or slightly yellow) it does miracles.