Batteries left connected during storage discharge for several reasons. The main reason is that the batteries will continue to power the CO, gas detectors etc. and over time this will discharge then. Also, these batteries will self discharge over time. A discharged battery will sulfate its plates which will degrade its performance. These batteries use sulfuric acid which is actually an oil and doesn't freeze, even when mixed with equals parts water. As the battery discharges, much of the acid is converted to water which will freeze. As this water freezes it expands causing physical damage inside the battery and permanent damage.
Fully charged batteries resist sulphation and have sufficient acid to prevent freezing.
Your unit likely has a "trickle charger" to maintain your battery when connected to shore power. Some units have a smart charger which regulates the charging current at a correct level and may also have sufficient output to operate lights
and other trailer options at the same time.
The best way to maintain the battery is to keep it properly charged. Flooded lead acid batteries will require the addition of distilled water, AFTER CHARGING. If your unit has a smart charger you can leave it connected to shore power, however your battery must be connected to your unit and this means your gas detectors are also energized. This may shorten their life depending on their construction.
I suggest disconnecting the battery during storage and using a smart charger to maintain it at a correct level of charge. Debris on the top of the battery can cause a short between the terminals which will discharge the battery. I would recommend against covering the top of a flooded lead acid battery with plastic as they liberate explosive hydrogen gas. I've seen two of these explode, distributing pieces and acid over a 30 foot radius. This may not be a problem with other types of batteries.