Fully charged batteries will be just fine. If you chose to leave them on the TT, and not plugged in, make sure they are completely disconnected from any power drain. Best thing mark which wire(s) is what, and disconnect the power leads. You can leave the TT plugged in all winter too. If you do make sure to check the fluid level, if you need to add fluid, only add DISTILLED water, nothing else.
I remove my battery, and place it on a board on the floor of my garage. Usually I check them once or twice each winter. Usually in the spring they ares down 0.1 or 0.2 volts, but my batteries are now about 8 years old.
2012 Jayco X23B
2020 Ram Laramie 3500 SRW Air ride 50Gal fuel tank.
2007 Dodge Dakota Quad Cab (retired from towing)
Equal-I-zer 4-Point Sway Control