MY HORSE HAS A COUGH AND A RUNNY NOSE. WHAT DO I DO?
The first thing I would do is take the horses temperature to determine if he/she has a fever. If indeed your horse has a fever I would administer an anti-pyretic like phenylbutazone and some broad spectrum antibiotics. If your horse has no fever and is eating I would wait a day or two to see if the discharge resolves. If it does not I would contact your veterinarian to evaluate and scope your horse.
all the best