“The Hot Stove League has been keeping up its usual gait this week in baseball matter but for some reason or other Milwaukee has been sidetracked by the dreamers.” The Milwaukee Journal, November 2, 1901, p12
Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1908. “This situation [that the New York Giants will win]…will give the ‘fans’ something to talk about when the Hot Stove League opens its season” (The Sporting Life, Sept. 19, p. 3; Stuart Y. Silverstein).