This well insulated, very small building is called a home dairy. These home dairies are all over our area on old homesteads. This one dates back well before the 1940s and is a "young" dairy. There are many older ones around. Many of them sit lower to the ground and have been converted to storage or as chicken or rabbit houses.
When the home this one is located at was sided, they sided the little dairy too. As a result, this dairy is HEAVY! While outhouses were set far from a home due to the odors, these were set relatively close to the home.
People used these well insulated buildings to store their milk while waiting for the cream to rise. The shelves were for half gallon bottles and jars. The bottom part was for larger containers like buckets and pans. They'd put thin towels as covers over the containers.
Milk took up a lot of room while waiting for the precious cream to rise, so these little buildings helped free up space, keep the milk clean, and kept the milk from being knocked over. It's basically a safe for that period's very precious home commodity.
I was able to milk our goats and put their milk directly into the refrigerator. I didn't have to worry about spoilage and could take my time waiting for the cream to rise. I can't imagine having to run outside to check it. Even though I love modern conveniences, I'd still like to have one of these building on my farm. I think they are a neat little piece of history!