If you had a refrigerator, the freezer compartment was very small and held a couple of metal ice cube trays and _maybe_ a pint of ice cream.
Mostly, city folks had real refrigerators.
In the 30s? I lived in the city as a kid in the early 50s in a middle class area and hardly anyone we knew had a fridge. Everyone had ice delivered by the ice man every few days. I walked to the store with mom just about every day since the ice boxes weren't the best for keeping perishables very long in the summer. c
We had one of those that never would die so we could get a new fridge. That little freezer compartment had a door and constantly had to have the ice build up chipped off. We did have an upright freezer... in the bathroom. Ugh, that bathroom was so old. One day I couldn't stand it anymore, so while everyone was at work, I peel 'n stick laminate tile and tiled the floors, the sink and counter, around the tub (that had that awful green fake tile wallboard), and as far up the wall until I ran out. It wasn't until the year after I'd graduated that they finally moved into a brand new house and bought a new fridge.