Refrigerator on or off while towing your trailer?

Is it a problem to tow with my refrigerator turned on? I am planning some longer trips and would like to keep my food cold, worried about baking in the trailer all day while traveling will warm up some of the parables to spoil them. Any risk to damaging the refrigerator?

On; set to Auto so the compressor runs on the Propane. You have to turn off propane for certain bridges/tunnels but otherwise I always keep it on. But I’m new to this, so I welcome others’ advice!

Ya, don’t run the fridge on propane that is a bad mistake. Many many people do it for years successfully, however fire DO happen. To many safety issues that could happen for me to do it. I have a inverter in my rig so I can run it via AC but for most short trips the fridge will stay cool easily for 12 or more hours. The key is to keep the fridge and freezer full with a mass. We keep bottled water frozen in the freezer and in the fridge and put as much as we can in as we pull food out.

I have a older version of this and a set of rechargeable batteries to run this fan. You can hear it running in the living room so I eventually upgraded.

I ended up getting one of these and it helps cool down faster and keep the fridge cooler longer:

https://rvcoolingunit.com/Dometic-3-fan-Special-Deluxe-Fan-with-LED-lights-15-34-inch-wide-P5661663.aspx