Perhaps in "equine circles, the colour of a horse is its SKIN colour", but as was noted above, not as commonly used in the USA. How would one be able to identify the color from a distance? Unless you riffle the hair, you don't know what color the skin is. A 'white' horse, however, *could* be called a 'grey', simply because *most* white horses start out grey or even darker; many horses pale as they mature.

If I'm not mistaken, a horse, just like a dog, has different colors and shades in different parts of the body, depending on the color. For instance, white legs on a horse denote white skin beneath, as well as -often - a white hoof.