>>18105014
If they had some powder they could have gotten rid of any residue with that. Rubbing dirt or mud on your body actually does get rid of loose skin and whatever other particle are on your body.
Fresh clean water would be a huge problem for a standing army at that time. And bathing regularly actually removes natural oils from your skin. Most people don't realize this if they never spent enough time outside to realize that bathing makes you sunburn easier. Makes it easier for bugs to bite you. Dries out your skin after the moisture evaporates and now you have no skin oil keeping your skin damp.
It seems they might have found a way to prevent all this while also not smelling like rutting pigs and having all kinds of marching sores.