The short answer is "yes", but you need to know a couple of simple things:
Tow weight limit for the '03 is 5,000# with a weight-carrying hitch. If your trailer is over 1,000#, it must have brakes.
You need to watch the tach and learn to identify when the torque converter has unlocked itself. When this happens, the torque converter will churn the ATF, causing the tranny temp to rise. If allowed to continue, this can overheat and damage the tranny.
An rpm jump of 200-300 indicates the converter has unlocked. This will happen when you need more torque to maintain speed, such as when climbing a grade or towing into a headwind. If the converter stays unlocked for any long period (over a minute or two), manually shift to 4th, which will allow the engine speed to rise and the converter to lock up again.
It's a good idea to manually downshift when you see a hill ahead that you know the 'Runner can't handle in OD. Do your downshift before you start climbing the grade so that the engine isn't yet at a high throttle setting.
Also, of course, learn to manually downshift on long downgrades to avoid brake fade. The rule of thumb is to choose a lower gear that'll let you descend the grade while maintaining your speed without using the brakes.
I towed an old Porsche 911 on a lightweight open trailer (4000#) for ~20,000 miles with Ralf, our '03 V8 LTD 4WD. It was a nice tow rig, and would manage 14 - 15 mpg. This past winter, I bought a new car and a new closed trailer (tow weight 5500#, pushes a lot of air). My mpg dropped to 9 - 11, and Ralf could no longer tow in 5th (OD), so I put Ralf up for adoption and bought a V10 diesel Touareg which delivers 553 lb/ft of torque. I'm eagerly awaiting my first tow!
Good luck with yours.
BTW, I have a new set of front brake pads, an engine air filter, a cabin air filter and a couple of oil filters for an '03 V8 that I'd like to sell. These are all Toyota OE parts. If you're interested, make me an offer at:
[email protected]ust
-Karl