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