For the better part of American History up to the mid-20th Century, the cast-iron stove was the primary heat source for homes and businesses. Through the long Winter months, people would gather around the stoves for hours the way they gather around TVs today.
So the use of the term today brings back images of groups of men in bars, general stores or other popular gathering spots, huddled around the warm stove, talking passionately about their team, discussing their needs for the coming season and sharing the latest baseball news.
Because baseball fanatics can't stop talking baseball. Similar to someone who loves golf. He will talk people's ears off because he loves it so much. It's OK if he is with other golf lovers, but often he forgets that there are some people on this planet who don't know or care anything about golf, God bless their souls. To a lesser extent, some baseball lovers like to keep talking baseball during the winter when it is cold, so hence somebody came up with a great expression for these baseball lovers, "the hot stove season".
And it's up to the women folk to carry in the wood and coal to make sure the stove keeps hot while the men folk b.s. the winter away. It's a great season for sure.
Because the off season is in the winter and in the old days a lot of people heater their houses with wood or coal fired stoves
Time to sit around the stove and talk about the upcoming season.....!!
And then the men folk would gather around and talk about the upcoming season and their team.