Maybe a chest freezer would be easier to dig to the bottom of, if you set it up like our foot lockers at Boy Scout camp.
The footlockers had a shallow tray that sat on top of the main volume of the footlocker. That lifted out easily and revealed the bottom 3/4 of the contents.
Maybe keeping the top few layers of things in a chest freezer in boxes or heavy bags would let you lift out and replace things faster than digging and rummaging would.
I suspect they would collect frost while outside the freezer, but individual items would collect even more frost.
