Horse Coughing?

Nothing, they don't. If they did I'd be looking at the environment first. Dusty bedding or forage, ammonia from bedding/drainage, general dusty stabling, ventilation etc.
 
If they aren't in a dusty environment and I'm not happy, I would get the Vet to listen to the horse's chest. I did that once and the horse had a chest infection. Easily cleared up with antibiotics.
 
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