I have not brought a stroller since we had only 2 kids, and they were 3 and 1, and it was just me.
Fast forward to our 2012 trip and 5 kids deep. Our youngest were 3 and 6(just turned 6 while there). We were going to without using a stroller. We went to DHS first day, it was August 25th. DS5 (3yrs), was moving in slow motion, not complaining, we weren't moving fast, but he face was butt level with everyone, dragging a little behind. We felt like he was being dragged which he was not. This is a kid who does 6 flags all day long without a stroller. But with the heat of the ground under his feet, the heat of the air, the crowds, we decided to rent a double at Epcot. We did it for length of stay, we hopped everyday, so when we hopped we would give our stroller to another family upon exiting, and pick up another at the next park. Both the 3 and 6yr old were it.
What was best, was that August is hurricane season and yes Ivan hit while we were there. It was easy to get around quickly during a down pour, they stayed dry and happy. With 5 kids, 2 were in the stroller, the oldest often pushed while the other 2 walked along side, and dh and I would hold hands behind them, admiring all our boys! They were easily located that way too.
You will know what will be best for you and your little ones. When we go this year the youngest will be 5 and 8 (just turning), so we will try again to go stroller less.