The problem you will have is that you have no supplementary power to the caravan whilst towing so no 12v to fridge or to the battery for charging. It depends whether that is important. If it is the easy answer would be to fit or get fitted a grey s socket to the car.
As Grampian says it is a matter of choice.
We always use our fridge on the move. If you go abroad you might want to take English goodies like bacon in the freezer.
I would have thought it was worth phoning a mobile fitter for a quote. Probably not more than £40/£50.
Daves1
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.