The Magical Beginnings program was introduced last year -- August and September -- to entice families with preschoolers to plan trips for that time of year.
This year it's running September and October.
Last year there were special concerts and shows at MGM geared towards preschoolers, and MK had Little Ones EMH mornings, where only Fantasyland was open, for onsite guests. They had plenty of characters on hand to entertain and play with the guests. It was held three days per week last year, in addition to the 'regular' EMH morning at MK. So, it's definitely something to plan for or around. They haven't announced the details for this year yet though. So, we don't know if/when EMHs will be.