In the United States today, I believe, "hot stove league" is used primarily to refer to off-season discussions about baseball.
The Dickson Baseball Encyclopedia, third edition (2011), cited in Josh6's answer, gives a first occurrence date for the term "Hot Stove League" of 1908:
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).
I don't find a reference in this dictionary entry to the claim that "Hot Stove League" was first applied to baseball in 1897.
In the Library of Congress's Chronicling America newspaper database finds its earliest match for the term "hot stove league" in 1908. From "Base Ball Notes," in the [Washington, D.C.] Evening Star (December 30, 1908):
The handicap billiard tournament for the championship of the Hot Stove League is drawing to a close at [John] McGraw's in New York. Christy Mathewson and Sammy Strang will play a "double-header" with McGraw this afternoon. Yesterday, Charley Atherton, who seems to be the "class; of the tourney and likewise "scratch" man, defeated McGraw 100 to 50.
All of the named individuals were baseball players, and three of them played for or managed the New York Giants in 1908.
Three days later came this cartoon caption in the Spokane [Washington] Press (January 2, 1909):
Around the hot stove the drafted bush league phenom tells an admiring audience what he will do to the big leaguers.
The next winter the Wenatchee [Washington] Daily World (December 9, 1909) had a roundup of midwinter baseball news headed "The Hot Stove League," and on March 14, 1910, the [Washington, D,C,] Evening Star published "Won in the Ninth"—"a base ball story" by Christy Mathewson—the Hall of Fame pitcher and erstwhile billiards player—that includes this passage:
And so they talked and talked until long after time to be in bed, and told all the stories about the great Lowell clubs of the past, the great pitchers, the catchers and the fielders, and the fellows called it the first meeting of the Hot Stove League of Lowell University, 19—. This talking league lasted through part of February, by which time the freshies who had done wonders on the high school team at home, and who had come to Lowell with high hopes of making the team, had a pretty good idea of the kind of enthusiasm and loyalty and, most important, hard work they would have to show to get on the team at Lowell.
And finally, the [Washington D.C.] Sunday Star (November 20, 1910) published a poem called "The Hot Stove League" that closes with these lines:
What if their plays are built of smoke and laughed to scorn by men?
They have but to light their pipe to play them o'er again.
There are no dubs in the Hot Stove League, every guy is a star, by jove,
For every galoot slams the ball in the snoot—around the old hot stove.
Ah let them play their games in dreams, with never a fault or bull,
With one-hand grabs and double-plays and home runs with the bases full.
But what a corking team we'd have if we signed up every cove,
And they all played ball like they do in the fall—around the old hot stove.
As these various quotations suggest, a "hot stove league" in the early 1900s was not necessarily preoccupied with major league baseball. Local talent and local teams could be as much a focus as the top baseball league, depending on who was doing the discussing, analyzing, or reminiscing.