I would have thought a trailer of that size might already have electric brakes with a battery and safety breakaway switch. I'd put a larger battery in for that (assuming it's just dinky little one to begin with) and use that for the winch. If it doesn't have brakes, or has electric brakes but no breakaway switch, I'd add those parts. Obviously, if it has surge brakes, things are different.
As for a connector for the truck, should one go that route, I think the usual connectors are the "quick connect" connectors also used for semi-permanent jumper cables often equipped on tow trucks etc. (where there's a connector on the grill of the truck that the other half of the cables plug into).
Here is one example (but please note that I don't know if these particular ones are great, or junk, or something in between).