Just because you take the power away from it the fridge is not going hot in the next half hour. It is no different from losing power in a storm. You are good for hours.
If you don't have one already, get an inverter large enough to comfortably handle the fridge. Of course that inverter is of little use if you don't you don't have the battery bank to support it. The TV will charge, or attempt to charge, the trailer while going down the road. The weak link there is the distance from alternator to trailer battery bank & the thickness of the wires. VD, voltage drop. Make sure that the inverter is not feeding anything else in the trailer to get longest life out of the battery bank as you roll down the road.