I can't access the OED at the moment, so I don't know to what extent this is covered there, but via newspaperarchive.com I found an interesting article relating to the use of "cool" in the jazz world, in the Bridgeport (Conn.) Telegram, July 13, 1948:

begin

"Hot jazz is dead. Long live COOL jazz!"
That is the startling statement attributed to Leonard Feather, self-styled jazz expert, in a publicity release ...

"Hot jazz, as such, may be on the way out," says Feather, "but it is gradually being replaced by something that can just as well be described as "cool jazz." This phrase is simply a way of describing the younger musicians' new approach to jazz improvisation.
"The old-school jazz created a tension, where the new jazz tries to convey a feeling of rhythmic relaxation. Jazz today tends to be played a fraction behind the beat, rather than right on the beat or even ahead of it."
The term "cool", he points out, is used by many musicians as a synonym for everything good. As examples of "cool" musicians, he cites pianists Dodo Marmarosa, Errol Garner; tenor saxmen Lester Young, Lucky Thompson, Wardell Gray, Allen Eager and Dexter Gordon; alto saxist Charlie Parker, trombonist J. J. Johnson and guitarist Barney Kessel.

In other words, Mr. Feather feels that nothing but the "bebop" type of jazz is worth bothering about.
That we disagree wholeheartedly with Mr. Feather need hardly be pointed out to anyone who listens to our "Rock 'n' Rhythm" program over WNAB these Tuesdays at 7 p.m.
On "Rock 'n' Rhythm" tonight, we are planning a battle-of-music between the "hot" and "cool" types of jazz.

end

This is interesting for a few reasons. First, Feather's understanding of "cool jazz" seems related to, but not entirely the same as, the idea of "cool jazz" that began to emerge a year or three later. Feather's "cool jazz" seems to be somewhat bogusly defined, but it's hard to see how it's different from bebop (one wonders whether he was searching for a term to replace 'bebop' or 'bop').
Second, note the name of the Bridgeport show, "Rock 'n' Rhythm". This shows that "rock" was being used in a jazz/blues sort of context and presumably refers to the conservative danceableness of the music played on the show (I'm basing this in part on the hostility the writer shows for Feather's point of view). I've noted before that the very term "rock and roll" can be traced back to the late '30s or early '40s and the idea that this was originally a sexual term that came to be applied to music seems to be a total self-serving myth created by the champions of certain post-Suez musical styles.
Early rhythm 'n' blues, as a style of music distinct from swing or jazz generally, seems to date from this period, and of course that black musical genre was the direct ancestor of the white "rock 'n' roll" genre that emerged after the Suez Crisis (with some hillbilly influence thrown in). I can see how rhythm 'n' blues would have been seen as "hot" in a different way from how the revived Dixieland was "hot". Cf. the "hard bop" style of jazz that developed in the mid-1950s sort of in aesthetic opposition to the cool jazz and West Coast jazz of the early '50s.

Third, Feather reports that musicians were, by this time, using "cool" to mean "good", though I guess we already knew that.
I can't access the OED at the moment, so I don't know to what extent this is covered there, but ... Feather reports that musicians were, by this time, using "cool" to mean "good", though I guess we already knew that.

The relevant OED entires (with early cites) for 'cool' are:

d. Applied to jazz music: restrained or relaxed in style; also applied to the performer; opp. hot a. orig. U.S.

1947 (record by Charlie Parker Quartet, Dial 1015) Cool Blues. 1948 Life
11 Oct. 138 Bebop: New Jazz School is Led by Trumpeter Who is Hot, Cooland Gone. 1950 Christian Sci. Monitor 8 Feb. 15 Bop is 'cool' jazz in contrast to the 'hot' variety of the swing or Dixieland schools.

e. Hence, characteristic of those who favour 'cool' music; relaxed; unemotional; also used loosely as a general term of approval; cool cat: see cat n.1 2c. colloq. (orig. U.S.).

1948 New Yorker 3 July 28 The bebop people have a language of theirown.+ Their expressions of approval include 'cool'! 1953 Time 14 Sept. 68/3 The latest Tin Pan Alley argot, where 'cool' means good, 'crazy' means wonderful.

John Dean
Oxford
I can't access the OED at the moment, so I ... to mean "good", though I guess we already knew that.

The relevant OED entires (with early cites) for 'cool' are: d. Applied to jazz music: restrained or relaxed in style; ... include 'cool'! 1953 Time 14 Sept. 68/3 The latest Tin Pan Alley argot, where 'cool' means good, 'crazy' means wonderful.

"Cool jazz" also refers to a particular style within bebop. I quote from The 101 Best Jazz Albums (1980):
Once jazz had become modernized (in the late 40's), it began to become diversified into styles known as "cool," "West Coast," "third stream," "progressive," and "hard bop." ... Cool jazz was characterized by a clean, vibrato-less, and studied tone placed within a meticulously articulated musical environment. If bebop had been an intuitive outpouring of energy, cool jazz seemed to say, "We are now artistes ; we think, therefore we play."...(Claude Thornhill's) band was also the model for the Miles Davis nonet, whose Birth of the Cool (1949) was the first album in this style.

(Me again) I wouldn't be surprised if the OED's dates could be pushed considerably further back into the 30's, say.
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"Cool jazz" also refers to a particular style within bebop.

It depends on how narrowly or broadly you define "bebop". Often "bebop" is used to describe specifically the earliest, pioneering phase of post-swing modern jazz, and as such bebop gradually disappears in the early '50s as it evolves into several child styles (cool jazz, West Coast jazz, hard bop, modal jazz, etc.). In one sense, the whole understanding of what jazz is is completely reshaped by bebop, so that bebop can be seen as the phenomenon that gives birth to all modern jazz.
There's a broader way of looking at bebop (maybe "bop" is the better term to use) as the whole main stream development of jazz since 1945. In that sense, the various subsequent styles can be seen as particular varieties or later forms of bop/bebop, though I think there's a point where a subsequent style can deviate so much from the basic aesthetic elements established in bebop that it no longer makes any sense to consider that style bop or bebop.
In the narrower definition, the subsequent "hard bop" style is seen as being more aesthetically faithful to the original bebop, in contrast to cool and West Coast jazz (sometimes treated as synonymous).
I see that it is time for more "cool".
Here is another Zora Neale Hurston quote from Spunk in 1935 to add to those that Ben Zimmer found earlier:
LINA (laughing) That's the baby's guitar.
ORAL. The baby's guitar*
SPUNK. Yeah, man. I made it at the mill today. I'm not going to let my son sit up in the cradle and ask him daddy 'Papa, how you let me come in this world without no instrument to play on?' So I done made it already. Man, by the time he's ten years old I'be be shame to play in front of him. And what make it so cool, he's going to look just like me.
Richard Maurer To reply, remove half
Sunnyvale, California of a homonym of a synonym for also.
I can't access the OED at the moment, so I ... begin == "Hot jazz is dead. Long live COOL jazz!"

The relevant OED entires (with early cites) for 'cool' are:

1948 Life 11 Oct. 138 Bebop: New Jazz School is Led by Trumpeter Who is Hot, Cool and Gone. 1948 New Yorker 3 July 28 The bebop people have a language of their own.+ Their expressions of approval include 'cool'!

Looks like 1948 was a breakout year for "cool". But it really hit the mainstream c. 1952, when white teenagers across the country started using the word. I mentioned the 1952 movie "A Young Man's Fancy", with a slang-slinging teenybopper calling her crush "really cool" (and "a real cool Jonah") (1). That same year, "cool" was recognizable enough as teen slang to be included in numerous comic strips (which are also searchable on newspaperarchive.com):
Muggs and Skeeter, May 5, 1952
"Gee, I like your pipe, Gramps! It's real George and ricky-ticky!"
"It's real what... and what?"
"Real George and ricky-ticky!!! That means it's cool... real cool!! You know, hot stuff!"
Our Boarding House with Major Hoople, July 31, 1952 "As the younger generation would say, Major, that's real cool!"

Honeybelle, December 13, 1952
"Senorita, get hep, and you'll be mine in starlight time!" "Cool! Real cool!"
(1) http://groups.google.com/groups?th=f86ca5675fe84f81
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I see that it is time for more "cool". Here is another Zora Neale Hurston quote from Spunk ... shame to play in front of him. And what make it so cool, he's going to look just like me.

Thanks for that one coincidentally, I came across it recently on the Library of Congress website, which has the text to all her plays (I'm guessing that's where you found it too):

At first I thought it was actually from 1925, but it turns out that Hurston just wrote a short story called "Spunk" that year, and the play was published ten years later. I checked the short story, and the line isn't there. So the citation from "The Gilded Six-Bits" (1933) is still the earliest appearance of "what make it so cool" in her works. Here are the other examples I've come across:
And whut make it so cool, he got money 'cumulated. "The Gilded Six-Bits" (Story Magazine, 1933)
De best in de State, and whut make it so cool, he's de bes' lookin'.
Jonah's Gourd Vine (1934)
"Got yo' guitar wid you, Johnnie?"
"Man, you know Ah don't go nowhere unless Ah take my box wid me," said Johnnie in his starched blue shirt, collar pin with heart bangles hanging on each end and his cream pants with the black stripe. "And what make it so cool, Ah don't go nowhere unless I play it." Mules and Men (1935)
"Now me, wouldn't let you fix me no breakfus'. Ah git up and fix malt own and den, whut make it so cool, Ah'd fix you some and set it on de back of de cook-stove so you could git it when yo' wake up.
Mules and Men (1935)
"Why you say dat? Ain't I got de prettiest wife in de world. And what make it so cool, she's de sweetest wife God ever made."
Mules and Men (1935)
"Y'all lady people ain't smarter than all men folks. You got plow lines on some of us, but some of us is too smart for, you. We go past you jus' like lightnin' thru de trees," Willie Sewell boasted. "And what make it so cool, we close enough to You to have a scronchous time, but never no halter on our necks. Ah know they won't git none on dis last neck of mine."
Mules and Men (1935)
"He was top-superior to the whole mess of sorrow. He could beat it all, and what made it so cool, finish it off with a laugh."
"High John the Conqueror" (1943)
Hurston also wrote a glossary of "Harlem Slanguage" (included in The Complete Stories ), but "cool" is not listed. Interestingly, it does include "cold" as an intensifying adverb:
cold , exceeding well, etc. "Yeah man! He was cold strolling on that trumpet!"
That use of "cold" is similar to "stone" as an intensifier (beyond the similative usage of "stone cold", "stone dead", etc.). Hurston supplies an early example in Mules and Men : "You must be stone crazy!"
"Cool jazz" also refers to a particular style within bebop.

It depends on how narrowly or broadly you define "bebop". Often "bebop" is used to describe specifically the earliest, pioneering ... being more aesthetically faithful to the original bebop, in contrast to cool and West Coast jazz (sometimes treated as synonymous).

Which then segued into progressive jazz via efforts like those of Dave Brubeck, Shorty Rogers (soundtrack for "The Wild One"), and many others.

dg (domain=ccwebster)
Areff filted:
"Hot jazz, as such, may be on the way out," says Feather, "but it is gradually being replaced by something ... tends to be played a fraction behind the beat, rather than right on the beat or even ahead of it."

Nice...of course, some twenty years or so earlier, the opposite of "hot" as applied to jazz (the stuff Kay Kyser played before he got into the novelty rut) was "sweet" (think Guy Lombardo)..r
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