I mean there is this general idea of it being introduced in the time period of 1950s to 1970s, but exactly in which issue did he use it for the first time?
An audio podcast on manofsteelanswers.com (#49, "Breath") lists several "first instances", depending on what you consider to be the "actual power" or "comic writers messing around".
Super-breath as in "expelling way more air than your average Joe could" first occurs in Action Comics #20 (January 1940), with Superman literally blowing out a villain's torch. The podcaster argues this might not be super breath, but rather super-strength applied to breathing (helped by his lungs being seemingly able to withstand the pressure of underwater dive, when searching for a sunken ship in Action Comics #15)
Super-breath as in "definitely not human" first occurs in Action Comics #37 (June 1941) when Superman extinguishes a fire in the mayor's office. Once again, as pointed out in the linked podcast, it's a tad bit ambiguous, as other future comics have fire "often being an obstacle, or threat". Several instances of one-time super-breath of sorts are quoted.
Freezing breath "for real" first occurs in Superman #129 (May 1959), once again to take out a fire, this time in the Superman Museum. The "super-breath will cause super-cooling", covering all the room in ice.
Expelling cold breath occurs in World's Finest #64 (May 1943), where Superman flies into the stratosphere, inhales the cold air there, and blows it out on the issue's villains, freezing them. (if I am to believe Wikipedia, this air would have been around -3°C/26.6°F if taken at the top of the stratosphere)