You can do as I have and buy 80 dollar inverter or spend more and get a giant one but, all you need is about 700 - 1000 watt inverter, connect to one of your batteries and run extension cord hidden under the unit or through the walls to reefer compartment.
Your batteries are being charged full time from your tow vehicle while in transit or even when you are parked and hooked to tow vehicle while idling.
Some of the later models even come with a dedicated 12 volt
circuit for a refrigerator. Dont be confused, I am not saying use this connection for inverter but the charge line is connected directly to your AS battery (s).
A little simple math,
new Dometic Reefer 900-1200 dollars (not frost free, takes long time to cool down and works best if full of articles, theromostat is sometimes tough to figure out)
new apartment reefer that is larger 8.0 to 9.2 cu ft, cools quickly, frost free, works great when empty and thermostat is reliable, never need new heater element, flue cleaning, ignitor, LP, etc...
400.00 dollars if you order online, 270.00 from Home depot or Wal-mart.
Inverter, Radio shacks best 1200 watt inverter 100 dollars!
Hmmm, now lets see,
700 dollars to be spent on new Honda EU1000 that can be used anywhere.