I'm going to post this as an answer because it's too long for a comment, but it's really just an extended comment.
The earliest instance I found in newspapers (from newpaperarchive.com) is from August 24, 1957, in the Alpine Sul Ross Skyline paper in Alpine, TX, in a story about someone in the Civil War. "Regardless how he met his end, he was a leader who kept his cool."
Also from newspapers (as background), from about 1921 on, in articles about sports, "he kept his cool head."
1927: "kept his teammates cool and at ease"
1928: "kept his cool-headed style"
1930: "kept his K___ team cool and collected"
1930: "kept cool and used his head"
1931: "kept his cool nerve"
1936: "kept his smile cool"
1937: "kept his brain cool"
1939: "kept his head cool" (also 1945)
1949: "kept his cool nerve, his patience, and his head"
1951: "cool style of play"
1952: "kept his Preston mates cool as cucumbers while the clock ran out"
1955: "kept his head cool"
1965: "kept his campaign cool and calm"
San Rafael Daily Independent Journal, September 23, 1965, "kept his cool"
1966 and later: "kept his cool"
Many of the above cases are multiple examples--i.e., there's a wire story that ran in several or perhaps many newspapers.
I'd conclude that "cool" as a noun is a shortening of adjective form--cool head, cool nerve.
June 1, 1958, New York Times Book Review, http://www.nytimes.com/1958/06/01/archives/pens-filled-with-protest-the-beat-generation-and-the-angry-young.html. This is a book review entitled "Pens Filled with Protest" of The Beat Generation and the Angry Young Men, ed. Feldman & Gartenberg (an anthology) and includes the following paragraph labelling "cool" an original word and connecting with the Beat Generation--Kerouac et.al.
Even American despair is optimistic; in Europe despair is cynical or
tragic. Beat, cool, hip, swing, square are emotive and original words,
and although the desire of the Beat to sharpen his own senses so that
he can concentrate and improve his dialogue with existence--not social
existence, however--often leads, in this volume, to outpourings of
self-pity and hysteria, it also leads to something less trite in