My dad told me similar stories. Hence the term ‘’icebox’’.
You’d get a big chunk of ice and put it in a large, usually oak box with a metal lined inside and that was how you kept things cooled.
I doubt anyone in America under the age of fifty has ever heard the word ‘’icebox’’.
The term lives on in "icebox cookies" (refrigerator cookies) or "icebox watermelon" (compact melon you can chill in the 'fridge).
My kids and grand kids have heard that term and explanation from me. I have always referred to what is now called a convenience store as an ice house. They all wanted to know why I did that. Hence the explanation of an ice box. I still have the ice tongs my dad used to carry the block of ice he would purchase from the ice house.
I do have early pics of my brothers and me standing in front of the ice box from the early sixties.