The container is not in the cave. You do not need to go near the cave entrance to find the cache.
Wind Cave is also known as Cold Cave because the temperature is close to freezing in the accessible portions of the cave. If you stand in the entrance, it is definitely chilly. See this article for more information about the cave. You do not need to enter the cave to find the cache.
Original hide: The ammo can is hidden somewhat out of sight of the cave entrance. You do not need to have rocks over your head when finding, signing, or replacing it.
Hide as of 4/26/2022: The ammo can went on a walkabout. Something smaller than an ammo can cannot stay in the original location. So we moved it slightly north and downhill. It is a camo'd peanut butter container on a rock ledge and covered with rocks. There's a reasonably open area in front of the ledge, and you will be comfortable standing there signing the log and putting container back with appropriate cover.