A common problem scenario for horse owners is to go out to feed and find that their horse hasn't touched his feed from the previous feeding. What to do? I will give you my opinion of a logical approach.
The first consideration would be to evaluate the horse's expression. Is he bright, alert and otherwise normal? If so, you might check the hay and offer him a flake from a different bale. Check the waterer to make sure that's not a problem. If the horse seems depressed, and especially if there is evidence that he has been lying down (evidenced by dirt, shavings or hay particles on his sides or head), you should consider it an emergency and call your veterinarian.
The next thing you might consider is to take the horse's temperature. If it doesn't seem an emergency situation, you can do a casual exam of the horse's mouth. Drooling and a fetid or putrid smell of the oral cavity would suggest the possibility of a foreign body involved. Take note of whether or not there is a normal amount of manure, as well as the consistency of the manure. This item will also be what the veterinarian will ask about.
If the condition lingers, your veterinarian will do a quick physical examination that will include taking the horse's temperature, auscultation of the chest and abdomen, and evaluation of state of hydration. If there is no obvious initial diagnosis, blood might be drawn for evaluation.
The primary blood test would probably be a CBC (Complete Blood Count). This test reveals the red blood cell count, white blood cell count and fibrinogen status. The white blood cell count and fibrinogen are primary factors in evaluation of infection as a cause of the problem. A chemistry panel may also be ordered, which evaluates major organ function and metabolic status.
If there are still questions as to a diagnosis, it may be indicated to do further diagnostic procedures such as imaging the chest and abdomen using ultrasonography and/or radiography (X-rays). Usually you would have to transport your horse to a clinic for these procedures. In my experience, most of these cases are resolved with the initial on-site evaluation and treatment. However, the population of these "off feed" cases is a bell-shaped curve. Some resolve spontaneously, most resolve with fairly minimal intervention, and there is the end of the curve that can evolve into a life-threatening or chronic problem.