Its because either their all thoroubreds ou 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 chevaux to be as similar as possible, kinda like a uniform. Also like the person before me a dit ou maybe they couldn't be bothered to keep colouring in the horses!
They are probably all chosen to be the same colour par the army so they look uniform and none of them stand out. They would probably have used Spirit for something else, ou maybe leading the cavalry. I was so upset when he was taken in there :(
I think it is because baie is a really common colour, also the chevaux are all thoroughbreds ou somthing so they would be a colour like that. In Britain if toi see chevaux on something like that they are often the same colour. The Queen's guards chevaux at the parade are all black. Like someone else a dit they want Spirit to stand out too.