Before you start on the oil, be sure that you are getting the horse enough nutrients including protein, copper, zinc and vitamin A. They are the top nutrients in putting a healthy, shiny coat on a horse.
For the oil, liquid oils are easy to mix in feed, and almost all of the oils with have a good impact on a horses' coat. Its a plus if they can be fortified with omega fatty acids. Coconut oil and rice bran have good omega fatty acids work well. And depending on what coat color your horse has, some oils, like molasses are pretty well known to darken coats. For example, will make palominos and duns go to more of a 'smutty' coat. But I would be sure that you don't feed molasses to a horse with laminitis or that have foundered before checking with your vet. Personally, flax seed oil is my favorite.