I live in Colo also and tow a 3600 lb low profile TrailManor travel trailer over our steep, long, and high altitude grades.
You might be able to tow the light trailer with OD left on; my experience is you best turn OD off anytime you're pulling a 3000 lb or heavier trailer. The key is whether or not the transmission torque converter stays locked...if it unlocks (you'll see about a 200 RPM rise on the tach when it does)...or if it downshifts to 3rd, the torque converter creates a great deal of heat. Additionally the constant engagement/disengagement of the torque converter clutch and OD clutch pack causes wear and even more heat.
One little known fact about turning OD off on the Tundra transmission is it will allow the torque converter to lock in 3rd gear...with OD on, the TC will only lockup in OD. With the TC locked in 3rd, I find I can pull up to 5% grades at 60 to 65 mph without having it downshift to 2nd...and a locked TC in 3rd gear provides enough engine braking that I seldomly need to use my wheel brakes on descents of grades of 6% or less.
I have a pan mounted transmission temp gauge and normally see 150 to 160 degree ATF temperatures when pulling hard with the TC locked in 3rd (ambient temps in the 70s) (when not pulling hard, the temp is more like about 130). But when the TC unlocks and I drop into 2nd for the steeper (6% or greater) climbs, the ATF temp fairly steadily rises to about 185 to 190...those are still acceptable temps but it's obvious an unlocked torque converter produces a huge amount of heat and heat is what kills a transmission. I should add that my truck does have the towing package with the external transmission cooler in addition to the cooler in the bottom of the radiator. If you don't have the towing package with that external cooler, you should immediately add one.
So to answer your question, try towing in OD...if you see even semi-frequent TC unlocking or downshifting to 3rd, just turn off OD and be done with it...as soon as OD is turned off, the transmission will go to 3rd and the TC will immediately lock.