If you are bathing her and she is still dirty, you are doing it wrong. Ha ha In between baths try getting her used to a vacuum. That really pulls the old hair and dirt off. Curry her good first and then use the vacuum to suck away the dirt. Obviously, this is when she is completely dry.
As far as the dirt goes, are you sure it is not just her color? I mean, are you actually seeing dirt or just that her coat is discolored? If that is the case, maybe a whitening shampoo is in order? I don't know what color your horse is so, just guessing.