Equine means having to do with horses. An equine saddle is one used for a horse, as opposed to one for a camel. An equine face is a horse face, and no, that's not a very nice thing to say.
Equine is connected to words that refer to animals—bovine means having to do with cows, porcine pigs, feline cats, canine dogs, etc. Many young girls go through an equine phase, where they are obsessed with all things horse—books, dolls, images, and, last but not least, actual horseback riding.