My asthma horse would have one cough, maybe 2, in the warmup. That was his only coughing. When the asthma is under control, there is no coughing under saddle. But some nose clearing (which is a good thing, if he doesn’t do it then he starts almost mouth breathing because his lower airway is constricted).
The one I have who is fussy in the contact sneezes a lot especially in canter. I’ve tried Zyrtec, nebulizer, allergy testing, no noseband, nose net (that was waaaay worse), and the different bits. It’s worse if it’s windy or dusty. And also worse when he’s behind the leg. Like he holds his breath. Because there doesn’t seem to be any therapy or equipment that makes a difference and I have no cough, I’m trying to address it from a training perspective (ignore the tossing and sneezing but trying to reinforce he’s got to go forward anyway). It’s super frustrating. He also can take the contact and work pretty nicely. He just would rather try the evasions instead. Which suggests something is wrong but I don’t have any idea. He also did get sore stifles at one point (he is growing), and we have tried support with ProStride and Adequan and it makes no difference with the front end things.