Once issued out of the Quartermaster's warehouses, foodstuffs and anything 'boxed' was shipped via covered transport or rail - usually to a siding.
If covered after that, it was covered by tarps or perhaps tents, and issued to requesting unit supply officers.
If that's followed - then outdoor storage under cover will weather the wood and new stencilling enough to look 'right' in a re-enactment setting, since rain will likely hit it, as will sunshine - dulling the formerly bright surfaces.
Ammunition boxes were generally painted - hardtack boxes weren't.
The hardtack box was ubiquitous, and useful, besides, and they 'still' show up.
Vaya,
Scouts Out!