In my limited experience with fivers, the Charge Line from the Truck (via the Seven-Pin Connector) delivers Very Little Power back to the Trailer. I guess Wire Size and Length contributes to this, and maybe the Truck's Voltage Regulator senses that ITS Battery (Under the Hood of the Truck) has been charged so it tapers voltage down to less than ideal for the long wire run to the Trailer.
What I'm saying is if we'd been dry camping, could drive all day, hundreds of miles, and NOT top off the Trailer's Battery Charge. What that implies is even if your Fridge is Three-Way (120VAC, LPG, 12VDC), running it on 12VDC will draw the battery voltage down and the charge line won't restore it. Low Voltage means Less Wattage means Less Cooling.