The sweet baby Jesus himself has literally answered the ops question at this pointLet's do the math on this. The simple math because when you consider this idea the way I'm going to present it you may have an "oh yeah huh" moment.
I get a real kick when people say you need a 9K to 12K winch to pull a 5K vehicle onto a trailer. First off, those winches are D rated meaning there's some fudge factor build in to the ratings. I would guess 20%.
So, can a 5000 lbs winch pull a 2002 Tahoe up a trailer? At a max weight of 5050 lbs that 5K winch can pull that Tahoe up the side of a building. People are worried about pulling a car up a 20 degree trailer ramp all of 5 feet long when it can pull a Tahoe 90 degrees straight up the side of a building. It's rated to pick their whole vehicle off the ground.
So, Unless you load your trailer by lifting the vehicle 3 feet off the ground then driving your trailer under it, I wouldn't be worrying about having a smaller winch.