Most important thing, disconnect the batteries from the camper. That alone will eliminate any accidental discharging of the batteries which can allow them to freeze. A fully charged battery will not freeze.
Leaving them hooked up and letting the converter keep them charged has 2 potential issues. One, the trailer could lose power. GFCI trips, breaker trips, someone accidentally unplugs it. I've seen it happen to my parents and their batteries froze (2 6V batteries). The 2nd potential issue is some convertors tend to over charge the batteries and cook off the water out of them. Mine does this over time, not real bad, but they need water every few months and I don't want to deal with that in the winter.
I used to bring my batteries into the garage each winter but I got tired of moving them around since they are so heavy, why not just leave them on the trailer? That is what I've been doing for the last few years. I do disconnect them and then run a trickle charger to them. I can get a glimpse of the green light on my Battery Tender Jr. hanging under the trailer and it is always just solid green, which means it is just monitoring because the batteries are fully charged. I also have 2 6V golf cart batteries on my trailer. I bought them in '09 and they still work great. Just camped the weekend for 2 night with the furnace on and still had capacity left.
To sum up, make sure they are disconnected from the trailer so nothing can drain them. Store them in a warm spot or leave them on the trailer. If brought inside, you can monitor the charge and charge as needed (you probably won't need to). Or leave them on the trailer and do the same. Or put on a trickle charger to make it a fuss free winter.
2014 Wildwood 26TBSS - Upgraded with 5200lb axles and larger Goodyear ST tires
2003 Chevrolet 2500 4x4 Suburban 8.1L 4.10's