Won't hurt the fridge..
Some units have a LAT switch (Low ambient temp) That turns on the inside light (incandescent) to generate a bit of heat inside the fridge which believe it or not makes it work better in cold temps.
I've been down to 11 overnight with no problem and no LAT (The RV was heated to 70 however by the furnace)
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times