The most common causes of equine respiratory disesae are Equine Influenza and Equine Herpes virus---what you describe could be either. Both are highly contageous and both often clear up on their own but they can also have very serious outcomes. Your horse needs to be quarantined and RESTED until all symptoms disappear. You should also be monitoring his temperature at least once a day--in the morning because outside temperatures will affect the reading.
Equine Herpes virus can mutate into a neurological form and is a HUGE issue. Influenza breaks down the physical barriers that help prevent respiratory infections and make secondary bacterial infections and deadly pneumonia more likely. Horses who have influenza are recommended to be rested for 1 week for each day of fever due to the damage it does to the lining of the respiratory tract.
There is no specific treatment for either of these infections because they are viruses, but your vet may recommend an anti-inflammatory to deal with fever and possibly an antibiotic if the nasal discharge has become mucousy which could indicate a secondary bacterial infection.
Licensed Veterinary Technician