The 1st doesn't sound familiar, but the 2nd does - was it down near Australia or is that a different one?
I remember yelling at the TV when the guy fell down in the snow "GET UP! AND MOVE IT soldier!" I also recall using the voice of authority at the TV when he brushed off the snow to the sign saying 45 miles this way, that "now", not "later", not in 10 minutes, was the time to start hoofing it. My heart literally broke because I was self-actualizing that situation. There were only two things that were motivating that guy's feets.
As far as the other, he went on to be the first double-amputee to climb Mt. Kilamnjaro. The show went on to say that the guide (amputee), and his "fare" remain good friends to this day. And as far as I understand he still goes into out of doors despite the ordeal he went through. And let me tell you, he went through some real bung-hole crap getting down that jungle infested mountain side as fast as he could.