OK, really old technique, but it still works.
Paint the horse overall in a light acrylic (white, light gray, tan), then use darker oil paint over the acrylic. Spot it on, then wipe it in the direction of hair growth. Horses are often lighter on the underside (like aircraft), so keep that in mind.
An Indian paint may not be the best one to start on. You might want to try with a more solid-colored horse first.
A few of mine.



The last one, a dapple, did not come out as well as I would have liked.