They also get allergies, seeds, dust and mold up their noses. I have a cow that blows and itches her nose all summer. Likely something she is grazing around. In winter time it stops.
A horse I have, had a chronic discharge from one nostril. Never cleared up with antibiotics. Turned out to be bad teeth. 3 teeth pulled and the drainage was gone.
Could be a number of things. But a temp would be helpful.