My Great Grandparents (my mother's father's family) died when my grandfather was 4; so what he knew came from the foster family (and other neighbors)?
What I heard: He was an enlisted soldier with Fremont when Fremont climbed Pike's Peak. BEFORE I knew about Genealogy, I looked up Fremont's expeditions (all that I could find). He DID climb a Mountain (but it wasn't Pike's Peak) but William T. Dorrance wasn't listed as a member.
Also, I cannot find any evidence of army enrollment (but that may be because I really don't know how to look)