Corn and vegetable oils are often fed to horses as a fat source. Oils can be fed to horses that have muscle problems, like tying up. A diet high in vegetable oils (high fat diet) is a cornerstone of therapy for this condition. Vegetable oils are valuable for adding calories to the diet and for increasing weight gain. These oils are thought to also have some protective effects on the stomach lining, and so are often used along with other medications for horses suspected of having gastric ulcers.
A common statement is that corn oil has a high level of Omega-6 fatty acids which actually increases inflammation. The fats that come from flax and rice bran have a more favorable ratio of omega-3 to omega-6 fatty acids, a less inflammatory mixture. That is the rationale used to favor them over corn oil.
Vegetable oils should be fed starting in small amounts, and gradually increasing. They are usually added to grain and in small amounts are palatable to many horses.