If the batteries are charged and disconnected, they also won't freeze over the winter (and won't self-discharge very much as the rate of self-discharge is heavily dependent on their temperature).
There's no problem with leaving the charger going, either, if it's a multi-stage charger. If it's not, it may be well to put it on a timer and have it run perhaps an hour a day or so (and, of course, also keep an eye on the electrolyte level in the batteries). It can be very nice indeed having power available in the RV if you have need of checking or doing anything in it.