The 1918-19 Flu Pandemic hit in three waves -- mildest outbreak was Spring 1918. Worst was when the flu returned in the Fall of 1918, with October being the most deadly month. That was followed by a third wave in Jan/Feb/Mar of 1919. People under 65 were the hardest hit throughout the pandemic.
If there is no season, it will be due to the players not wanting to risk infection. And the schools not wanting law suits. The ADs, TV folks, and coaches can stay 6-10 feet away from other humans, the players can't.