What To Do
If you notice that your horse is drooling, that is a good starting point for additional observation. Keep in mind that a few contagious diseases cause salivation, so be sure to wear gloves.
Offer the horse some feed. Is it interested in feed, and able to chew and swallow? Look for nasal discharge and feel around under and behind the jaw for swellings.
Assess the horse's general health using the Whole Horse Exam (WHE), paying particular attention to the rectal temperature and heart rate, and ability to chew and swallow. Assess the mouth as well as you can easily (wear gloves), looking for an obvious foreign body that you might be able to remove. At that point, you can share your findings and concerns with your vet.
What Not To Do
Do not examine a sick horse's mouth or attempt to treat without wearing gloves. Rabies is a rare but fatal disease that can cause salivation. It can be transmitted to humans through contact with a horse's saliva.