I'm not sure how heavily wooded Gila National Forrest is, but if it's anything like western WA then it seems it might be tricky to find a spot open enough to use a mirror effectively, especially if movement is hindered by potholing 2 feet of snow and considering an ill member of your party.

This story makes a good case for carrying some anti-nausea meds, especially if solo hiking. If Robert had been alone and "unable to move" as his son was due to the vomiting then the story probably wouldn't have ended as happily, seeing as it took him climbing up on a ridge and signaling from there to finally attract attention.