What would the LED work lights illuminate, the trailer tires? Unless you have an abnormally strong tongue jack system, you won't (shouldn't) ever have a vehicle on the trailer without the tow vehicle attached, so there wouldn't be anything on the trailer deck to illuminate.
I'm not sure that a single battery would have enough juice on it's own to do a 20' single line pull of a heavy vehicle up the ramps, without something charging it. Maybe instead of cabling something through your tow vehicle, have a set of long jumper cables from the anderson clip on the winch that can go up to the battery of the tow vehicle?
I'm bringing this up because a winch will be on my list when I get a car trailer. I absolutely see the benefit of a winch, but I don't see the benefit of having a battery.