You'll often hear folks speak about how racing does not have a beginning and end, like football or baseball does. That's certainly true. 365 days a year you can watch and bet racing, virtually 24 hours a day. This certainly does bother some, and despite the obvious differences (baseball and football are sports, while we are a participatory sport and gambling game), they have a point.
If we scan most racing related websites, it seems we do have a season, don't we? This is a 2011 look at traffic trends to DRF.com, via quantcast.
This works like clockwork each year.
When April rolls around we begin to see stories on nightly sportscasts, newspapers and the interwebs focus on the Derby. The Derby is watched and the winner is spoken about time and again. With the Derby winner fresh in the minds of the general public, and with only a two week gap to the second leg of the Crown (will the horse or won't he keep on the Triple Crown trail?), interest is still there. Into June, we still see interest in the last leg of the Crown, even if it's not achievable.
In addition, it does not matter who the participants are during our "season" just like it has little effect in football or baseball. Spectacular Bid or Secretariat could be the protagonists, or Mine that Bird or Animal Kingdom can. The spike and resulting wane in interest will be seen just like it will for a Super Bowl game between two little known teams.
If anyone asks me if thoroughbred racing has a season, I always answer yes. It starts in late April and ends when the Belmont winner crosses the finish line.