We've always had the 12 volt/ propane type. I think they worked on 115 volts too. Ours were always on while traveling. If your refrigerator doesn't automatically switch to propane when the RV is stopped, leaving it on 12 volts will drain the battery fairly quickly.
I will say that in my experience it is difficult to keep ice cream and frozen food frozen with the refrigerator turned off. We have never been able to, so we leave it on while traveling.
At home ours is turned off with the doors cracked enough to allow air to circulate. Paper towel rolls work for that, or whatever you can think of. If we were leaving for a trip I would turn it on several hours before loading it up, at least I did when I remembered it which was most of the time.