In the town where I live they allow us to park our RV's beside the houses. I've built a chat driveway with a dump station and electric hookup. I keep the RV plugged in all the time (with a good surge protector) and we often use the rig as an auxiliary to the main house. We keep stuff in the fridge and freezer and have, on occasion, used the RV as a guest cabin. During the winter (with previous RV's) I keep a small space heater set on the lowest temperature and the RV thermostat set to kick in as a back up if the space heater can't do the job. It's not unusual for us to take mid winter weekend trips so this system works well for us, as we don't have to hassle with winterizing and de-winterizing each time. I should mention that our northeast Arkansas temperatures don't get super cold, but there were times we hit 15 degrees and I have never had problems with anything freezing in the RV.
All this to say that in the twelve years I've had RV's, I've never experienced any battery problems that I could attribute to having the RV plugged in. I would think leaving the batteries hooked up might be the better option while camping since the system's trickle charge should keep the batteries at full charge.
2017 Thor Ace 29.4