It's your choice to use it or not. It won't hurt the truck either way, but with loads heavy enough to make your truck work hard, it will take advantage of gearing a little better in tow/haul. Basically just delaying shift points so the RPMS will stay in the sweet spot.
Personally, with my small 5k# trailer, I don't use tow/haul much when climbing hills. It just doesn't need it. But I use it on steep downgrades the most, because it improves motor braking.
Just don't use it in the snow in 2wd. Found out the hard way by accident actually. Getting off I-81 on the exit ramp. Kids yelling, dog barking at them, wife talking to me about something. Didn't realize I'd hit the button. Truck downshifted and got reeaallll sideways real quick. I always double check it now.
Clarify this a bit for me please,my 01 has the O/D button on the shifter(auto) now isn`t that the same thing as T/H mode? I use mine up an down hills or around town when towing heavy.Interstate being flat I don`t.
He may have been talking to me . What Bp said. The switch on yours only locks out the overdrive keeping you in third gear or lower. The T/H on the torwueshift changes the shift strategies holding gears for longer before upshifting and holding gears and downshifting when you are decellerating to help slow the truck and trailer without having to rely solely on the brakes to slow down.