Lots of debate on this topic. Some people do, others don't. I have always towed with the fridge off and everything in my cooler, however this last trip I towed with it on propane. It did fine, just depends on what you are comfortable with.
Keep in mind some places specifically forbid it (bridges, tunnels,etc).
I believe there is a poll going on this subject, but can't link it on my mobile device.
2013 Jayco JayFlight 26RKS
2013 Ford F150 Ecoboost FX4
2003 Coleman Bayside / 2011 Jayco Jayfeather X20E -- RIP
2012 Tacoma Sport DCSB / 2013 Tundra SR5 - RIP