Me and my friend dye her appy's mane and tail black all the time before big shows and we haven't had any problems. We get the least toxic wash out dye we can find.
We've also used it to brighten up the black stockings after a clip job and nothing bad has happened.
I wouldn't leave it on like you would for human hair, I wash it off the legs after it starts going darker.
I've been told that dog shampoos work better than horse shampoos do, so try and find a really good black one and try that first.