This is a heated topic, but I really think past the age of 4 most children should be able to walk the parks. Now before everyone jumps on me about hidden disabilities and whatnot, I mean children who do not have any type of developmental, physical or neurological delay or diagnosis.
My kids, who, by the way, are not particularly active at home, all managed to walk the parks from the age of five on. Even in the summer heat. Were they tired at the end of the night? Yes, and so was I. Did their feet hurt sometimes? Yes, and so did mine. Did they whine about waiting fro the bus? Yes, and so did I. Were they grumpy when I woke them up to get off the bus and walk to the hotel room? YES!
I know a lot of folks have expressed the sentiment that it is easier to push their kids in a stroller then have them whine and complain and ruin the families trip, but that is not the way things work here. Here adults make the decisions, and are not, generally, manipulated by children.