The best way to determine the adequacy of a already installed charging system between the tow vehicle & trailer is to actually measure the charging current under normal conditions. Find someone with a clamp on DC amp meter (Sears sells a relatively inexpensive one
that is also a multimeter that can measure resistance & voltage).
With the tow vehicle connected & the refrigerator
on 12V DC, run the engine at your normal driving RPM & put the clamp on meter around the wire going to the #4 pin on the 7 pin connector. If the current is equal to or over the refrigerator's draw, you system is adequate. If not, then improving the wiring is worth doing if you plan to run the refrigerator
on 12V while driving.
While measuring voltage gives you some idea of the charging system, it is not alway accurate since it depends on the the state of charge of both vehicle's batteries and other variables. The amperage measurement is more accurate.
I also suggest checking that the tow vehicle connection shuts off with the ignition. Some do, and some don't. A inexpensive solenoid can be added that will do it automatically, saving remembering to unplug during long stops.