Completely depends on what you show and how far you want to travel. There aren't specific dates unless you're talking about a specific circuit. I know people who go to the larger hunter/jumper shows who left for FL at the beginning of january. The first show of the circuit around here started this weekend but my first show prob won't be until the first weekend in march.
It depends on the area you are. Here you will start to see schooling shows at the beginning of march and shows continue on all the way until the end of fall. Some barns will run some schooling shows during the winter.