I have towed my 5er (Montana High Country) up many a mountain in western SC, NC, and eastern TN. They are smaller mountains than CO but can be fairly steep all the same. On open roads and interstates, I have literally done it with my cruise control on going up the mountian.
I did tow my 5er over a steep, narrow, twisty road (and I mean you can barely maintain a lane twisty) and got the transmission temp up pretty high. I was actually trying to see what the truck could do so I was getting on it pretty hard coming out of the switchbacks. It pulled like a boss and got a little workout in. If I backed off the throttle just a bit, the temp came down and was perfectly fine.
The reality is, going up aint the issue... its coming down where the biggest danger lies. Use your engine brake and take your time.