Welcome to JustAnswer. Let me ask you a few questions to better assist you.
Is your horse current on vaccinations?
Are the lymph nodes under its jaw swollen or abscessed?
It is most likely that your horse has an upper respiratory viral infection. Rhinotracheitis and Equine Influenza are common causes. If the lymph nodes are severely swollen and if the nasal discharge turns thick and yellow then I would consider strangles a possibility which can be more serious. I would recommend treating with sulfa antibiotics and Banamine. You will need to get these drugs from your vet. If the infection stays mild then you can probably get away without any specific treatment and just keep the horse sheltered from any harsh environmental conditions and away from other horses (to prevent spread as these viruses can be very contagious). The viral infection will typically clear in 10-14 days.
After the infection is cleared I would recommend vaccination. Rhino, flu and strangles are all diseases that you can vaccinate for to prevent future infections.
I hope this information is helpful. Please let me know if I can be of further assistance.