Your desire sounds like my zackly.

It sound exactly like what I am doing.
I have a hand crank winch on one trailer and it wears me out pulling stuff onto the trailer.
It isn't too bad if it was just one or two pieces, but I may have a number to do.
I want a winch mounted on the receiver hitch and be able to have the trailer hitched up to it for pulling stuff on and towing. I have several tow vehicles and several trailers that I would like to be able to interchange.
I'm still trying to figure out what to do for recharging the battery. I am fine with just putting a battery in the back and jumper cabling some wires to the winch for power, for now.
I got a solid piece of 2" square metal that goes into the receiver on the vehicle. Slipped over a ways and welded onto the back end of this goes a piece of 2" i.d. tubing that turns the back end of this into a receiver hitch. I got 2 pieces of square tube about a foot long to weld sideways onto the square piece to mount the winch to. I think that the 2" up will be enough extra height to get the winch cable above the trailer hitch latch. If you have a larger vehicle with extra height, you might be able to use a drop down hitch so the ball and trailer latch would be lower anyway.
It looks like the total length might be about 2 feet long, I can't remember right now.
I hope that extra length isn't enough to really mess with towing the trailer.
I expect that there might be some slop in the two connections so a trailer could get squirrel-y.
I'm not going very far and I don't plan to need to go very fast so I am sure it will work for me.