Seasons can have an Online Signup start date/time and end date/time now. That way you can control the specific time customers can start registering online (i.e. 9am rather than midnight).
To edit an existing Season, go to Programs > Seasons. Select your season and then press the Settings tab on the left hand side. The Sign Up Dates can be updated from within the "Registration Settings" section.
During the Season Export process you can set your times as well. The times will default to Start Date 00:00/12:00am and End Date 23:59/11:59pm.