As mentioned, the refrigerator while running on propane does require a battery connection for the electronics. Unfortunately there are a lot of parasitic drains on the battery while sitting so you should get in the habit of disconnecting the battery (most likely a dial switch in the front left compartment) whenever the trailer will be sitting for days without use. That will prevent your battery from running down and prolong battery life. I go a bit further an pull the batteries so I can easily charge them at home (I store remotely).
BTW, there is a forum here for Winnebago trailers, but a lot of folks do post just whereever, and this post was hardly specific to trailers. https://www.winnieowners.com/forums/f267/