@Deuteronomy of Gath said:

I really enjoy this type of action/thriller which takes place in a mountain/wilderness setting.
'Cliffhanger' and 'The Edge' are two others that come to mind.

Does anyone have any other recommendations?

First Blood! (Rambo, but it isn't like all the others). Also the start of one of the Borne films was really cool like this. Also there was a movie about a plane crash with wolves and stuck in the mountains but it was really bad.

Where Eagles Dare Last of the Mohicans Deliverance Touching the Void A Lonely Place to Die The Hunter White Fang Flight of the Phoenix (1965)

I thought of 5 more. Hunt for the Wilderpeople, Into the Wild, The Revenant, The Grey, Deliverance. There are a lot more on google if you search for movies set in the wilderness but these are the only ones I have seen. I did not like The Grey unfortunately and can't even remember Into the Wild. The others were cool.