My first camper was a late 1980's Starcraft slide in / pop up truck camper. It had a small 3 cubic ft 3 way fridge. Usually ran it on LP which did need 12v to power the control board. It would also run on 12v only but a fully charged battery lasted just a few hours. Hardly ever use the 120v option boon docking at the lake.
I've never seen a 3 way fridge in a pull trailer, I think they still use them in conversion vans.
Mike & Helen
2014 Voltage 3895 EPIC III
2013 Ford F350 CC DRW FX4