In the US Civil War, the northern (Union) army wore blue and the southern (Confederate) army wore gray. This is so well known in America, that in any story or song about the Civil War, all you have to do is mention blue or gray, and everyone knows which side you're talking about.
I don't think GOODBYE DOLLY GRAY is necessarily meant to be about the Civil War, though.
I don't know when the colors changed, but now the standard colors are olive drab or khaki. I think the Marines still use blue, though. I hope someone else will clarify this.