Its because either their all thoroubreds oder the people that made the movie want spirit to stand out so the audience is focused on him and not the other horses.
I suppose it's because (like in the cavalry over here in the UK) they want all the Pferde to be as similar as possible, kinda like a uniform. Also like the person before me sagte oder maybe they couldn't be bothered to keep colouring in the horses!
They are probably all chosen to be the same colour Von the army so they look uniform and none of them stand out. They would probably have used Spirit for something else, oder maybe leading the cavalry. I was so upset when he was taken in there :(
I think it is because bucht is a really common colour, also the Pferde are all thoroughbreds oder somthing so they would be a colour like that. In Britain if Du see Pferde on something like that they are often the same colour. The Queen's guards Pferde at the parade are all black. Like someone else sagte they want Spirit to stand out too.