I actually called the SWA 800 number to pose this question, since I've booked a 10/21 to 10/26 stay at WDW. I was told that the schedules would be updated at the end of June. This was last week around May 30th that I called.
I still keep checking, hoping it's sooner than that.
I can tell you that the information they give out over the phone is not entirely correct as far as when the site will be updated. I called once, was told it would be at least three weeks before the new schedule was released and when I checked a few days later, it had already happened. I missed the lowest fares because I had not checked on a daily basis.