every chance he wil catch something from another horse,when there being stabled so close to each other, i would first check his temp if he hot if he is around 38.5 then chances are he has cold, depending on the cough is it dry hacky type or sound s like it very deep with a rumble at the end, does he look depressed has he gone of his feed, i would also check his temp every day to see if it goes down thats if he has one
