All I can say is hook up and see. I regularly pull a 5x10 behind my '05 LJ Rubicon loaded to max capacity of the rig, which is 3500 lbs. I'm carrying everything in between from empty up to full load with the rig, from Jeep being empty, doors and hardtop stripped, to Jeep being fully street ready and loaded down and trailer loaded as well. In street trim, my LJ is pretty heavy at just under 5,000 lbs. empty, due to all my skids, armor, cage, bumpers, etc.
Drivetrain wise, I have the bone stock 4.0. Jeep did pretty well on it's own and I have no reason to change anything there. Running the 6 speed tranny. As to auto's-personal preference. If you feel more comfortable with the auto, go with that. I've been really happy with the 6 speed in my rig in all areas and wouldn't change a thing-on or off-road, towing or not.
Gearing-it did fine with the stock gears and factory MT/R's which were roughly 31's. When I bumped up to 255/85/16's -true 33's, with stock gears, it was AWFUL at best on it's own without the trailer. Lost 6th gear all together, 1st became a dedicated starter gear, lost all control and finesse off-road, what I could idle before began to take throttle-this is with a 4:1 low range mind you. I hated it, the rig was crippled with this setup for what I do. Towing a trailer with what I do was a joke. It did it, but hated every minute of it and fought me the whole way. I regeared to 4.88's and it's the best thing I could have done. If I ever go to 35's I'll wish I went 5.13's. With the 255's, the 4.88's are perfect in every aspect for me. Around town, on the highway, and towing. On/off-road, it just works. Got 6th back, can tow great again, off-road control/finesse is back again, the rig drives and handles like it should. Mileage improved as well with the new gears compared to stock gears and 255's as the engine is working in it's optimum efficiency range again.
As most tires tend to run small anyway and your 32's may likely be closer to 31's anyway, unless they're the 265's and even so, you may not have much to worry about. Like I said, I'd still hook up and see how it does. My 255's measure a TRUE 33"-actually 33.5" tall when new and mounted up so they're taller than most 33's and a fair amount bigger than 32's or 265's. Power draw or strain while towing with these compared to my brand new 31's on stock gears was definitely noticeable. I towed just fine on factory tires/gears when brand new (tires) so if your 32's are worn at all, the little difference there shouldn't be enough to put any real strain on your setup I wouldn't think. Again, hard to really tell for sure without hooking up and going for a drive. As the old addage goes, there's no replacement for displacement, but when geared properly, you don't need big horsepower to pull. My little 4.0 6cyl in my '05 LJ Rubi ain't putting out anywhere near V8 kinda hp numbers but I get up and down the roads just fine with my trailer within the rated capacity of the rig. The new trailer I'm building will target 1100lbs. empty as it's enclosed and built for off-road use. My current trailer is about that now, only larger and open.
Don't know if that helps or not, but something to think about.
Best of Luck,
Mike
