We were there for the first week of Nov 04. According to the weatherchannel.com, the weather was supposed to be high 50's/low 60's. As it turns out, we had low 70's/upper 60's and sunny about 90% of the time. We went to the beach house everyday. It was warm enough to spend two days playing and riding bikes on the beach. The rest of the days we spent at the beach house pool because it was sheltered by landscaping, so the cool breezes didn't bother us a bit.
We have a ds4, so we did mostly early dinners. By 5:00 or 6:00pm it was chilly and pretty dark. In the evenings we wore pants and light-weight long sleeve tops and were very comfortable.
We found there to be plenty of things to keep us busy. We were there to rest, so we spent the first part of each day swiming/playing at the pool/beach. We also spent a lot of time riding bikes and exploring the island. Went to a children's arcade/entertainment center (do not recommend it -- kind of yucky IMO

. Went to a movie. Shopped. Dolphin cruise from Shelter Cove(very nice). Visited Harbor Cove (the place where the lighthouse is ). Story time with Blou Crabbe (excellent). Campfire/smores (excellent). Pingpong, foozball, billiards (fun). Nice workout room. Kids fishing trip. Guided marsh tour.
This was our first visit to HHI. Overall we enjoyed the atmosphere, weather, activity. We would go back again -- even in November. We were lucky to get the Disney Visa $99 deal for a 2 bd villa. That made the trip all the better!
Have fun.