Most of what has been put here is good advice - with some good chuckles thrown in.  :-)
When we lived in Estes Park and were up in the Park (Rocky Mtn N P) we saw a guy in a car who used a lodgepole pine to stop after riding his brakes all the way down and they failed.  Cost him much more than a brake job.  Luckily, no one hurt.
Lower gear; don't ride the brakes.
One more thing.  Remember, gas engines lose power at altitude.  I am of the understanding - and heard it verified in the past - that a gasser loses 4% for each 1000 feet elevation gain.  I think that is accurate.
First time, many years ago, I drove a rented gas rv and was west of Denver.  It kept slowing down more and more.  I pulled over as I thought I had a brake locked up and went to check them.  Did not know the power loss thing then!