For the winch on my trailer, I ran #2 cable from my Dually's battery to a quick-disconnect at the rear bumper, to which the winch connects, and I mounted a battery in a plastic marine box to power the winch if I'm towing behind my other truck or SUV.
The Dually charges the trailer battery while towing, but if the trailer sits for a length of time I just put a tender on its battery.
Trailer battery is Group 24, 800 CCA.
About 15 years so far with no problems.