The best option, IMO, is to have a battery on the trailer that will run the winch, with max load. A far as charging, yes you can run the power wire from your trailer wiring constant power as a source to recharge your battery. But, consider draw. If you pull enough amps from the battery, it will continuously increase the amps being pulled from the charge wire. It's exceed the rating and or fuse for the charge wire, and blow a fuse and/or, melt the wire. You need a breaker system to keep that from happening.
If I were doing this job, I'd run a dedicated cable for both power and ground from the truck battery to the rear of the truck, to the same wire size as you have running from your trailer battery to the winch, using quick connects(Anderson connects) That way, draw isn't an issue, for multiple or heavy loads, you won't starve the winch for power which is a electric motor killer, and, it'll also have the best source of being charge/recharged you can ask for. A solar maintainer is good insurance to have a constant fully charged battery.
I hope this makes sense.