Colds and Influenza
Horses get colds just like people do, and treating the symptoms is the same: lots of rest, liquids, etc. Influenza usually manifests with cough and fever, and can be very contagious. In both cases, keep the infected horse away 
from other horses, and have the vet prescribe injections and antibiotics to prevent pneumonia.
Colic
Colic is severe stomach ache, or abdominal pain, for a horse. Usually it is the result of gaseous distension of the intestines, or tympany. It can also be caused by too much sand in the intestine, or twists in the intestines themselves. Usually the horse will show symptoms of completely collapsing, and often scraping his or her hooves against the stall wall.
Diarrhea
A horse’s droppings are usually firm, not liquid or yellow. Dark
colored urine is also a problem, and both of these are a sure sign of diarrhea. Usually this is a simple dietary problem.
Parasitic Disease
As an owner, you should check the fecal matter for worms every six weeks if the horse stays within that same stall. The general symptom is often a slow and listless demeanor. De-worming can be done orally with pills or injections.
Strangles
This is a common disease among horses. The symptoms include fever, nasal discharge, and abscesses in glands, mainly of head and neck.
This list is by no means exhaustive, and your vet should be contacted if your horse shows any ill signs.
Horse Breeds 
Horse Health - Medical 
