...was because they didn't have supply wagons but was relying on looting to get food.
Not much of anyone's speciality then - in the proper terrain cavalry has been capable of doing that since time immemorial (or at least since humans figured out horses were good for something else than the stew). Infantry too, they just aren't as mobile and can't ...forage (ie. loot and pillage) at equally long distances.

Only really doable with comparatively small units, however. Larger armies will need to split up if they want to do this (as most wanted and did) which has its own problems.