We used our stroller with our dd the last time, she was only 2. We haven't even pulled out our stroller since last summer, if then. She walks everywhere we go now. We went to BG and WC in Williamsburg in May and she did fine, never needed to carry her and didn't have alot of stuff either, just backpacks for each of us. When we go to Disney in the fall, we are going to go at her pace so if she gets tired or wants to take it at an easy pace, we'll accomodate that. So I think the way to decide is to figure out how much you actually use your stroller now for everyday activities, the mall, other amusement park type places. If they are still dependent on a stroller then definitely take it with you, if not, try going the first day to the first park and see how your little one does and then rent the next day in the next park if you have to.
Although having a stroller might help in the airport, if only to have a safe place for your little one while you handle business.