Keep in mind that doing a lot of walking around in a park like that for several hours is really hard on a disposable diaper. You might want to bring a change or two even if you don't intend to use, just to give yourself a chance to change out of a hot/sticky/sweaty/clumpy diaper, dry your skin, apply some cool powder, and get back into a fresh diaper to resume your enjoyment of the day. Otherwise, you might find youre somewhat miserable by the time you leave, have a diaper malfunction (centerline rip, tape failure, etc), or just plain decide to leave early because of some diaper-related issues.
(this, based on a similar experience I had in the past, mom walking me back and forth several laps around a massive shopping mall to do christmas shopping, I was quite miserable by the time we got back home)