Battery Storage

Leaving them in the trailer disconnected makes sense to me. They are Costco wet cell batteries.

My experience is that no matter how smart the charger, it will evap a wet cell battery over time if left connected 24/7/365.

IF....there is another reason to keep the shore power active....AND.....your Xantrex really DOES drop to a "float" voltage (about 13.2) or automatically disconnect itself as needed.....
Then leave it plugged in and don't worry about it.
If they are conventional wet cells, check the electrolyte level every 6 weeks or so.

The other replies are all correct too but no need to make it more complicated than it needs to be.

fully charge, and disconnect. Leave them in the RV.

I don't know what brand of batteries you have but I have 4 lifeline AGM batteries. When I bought them, I had the same concern. They told me to disconnect them and leave them in my camper. As long as they are fully charged when disconnected, they won't freeze and will lose 1%-2% charge over the winter months. If you have another brand or wet cell batteries, refer to what the manufacturer suggests.

I leave mine charging all the time.