My horse is fairly neat and stays mostly white looking most of the time. Even mud, once it dries, comes off of him pretty easily. He's also cremello instead of really "white" so he also has just a little golden tinge to him that I think also helps mask some dirt.
The worst part of having a white horse with pink skin is being able to see how dirty they actually are when you do decide to bathe them
It's very obvious if even a little bit of dirt is left behind when they're wet (but once the fur dries you can't tell anymore)