Coat'd Arms do a set of "horse colours". Most of them are OK although I've never got the dun colour to work well. They conveniently sell the horse colours in a pack now.
I also use a couple of Americana colours in grey-brown.
Generally I stick to those dark greys, browns and chestnuts; most of the horses I see are those colours. I figure other colours are rarer and hence probably prized and wouldn't be the nags you'd sell to the army
[1]
I just use those, mixing in a little white for the highlighting; don't over do it. Horses have a sheen which you can do quite well by just making sure you highlight in flat areas.
Leave the manes and hooves black.
Grab white, go round sticking socks and face markings on them.
Presto; horseses. picture
[1] No. I never wanted a pony as a kid. Don't like animals bigger than cats basically. Hence what I know about horses I find out from asking my lawyer (who is a horsey person) and from driving past fields of horses.