Sounds good to me. We usually carry a small first aid kit as well - plasters (I think you guys call them Band-Aids) and usually some antiseptic wipes, Aspirin and Ibruprofen in case either of us gets a headache while we're in the parks.
When we were there in December, we'd often start off in jeans and sweatshirts and when it got home, we'd take off the sweatshirts and tie them round our waists. We were usually OK like that. If we were feeling brave, we'd start off in shorts with a sweatshirt and just hope it warmed up later!