We like HH in late October / early November, BUT we don't go for the swiming.
At some point in late October, or perhaps November 1, they close the heated pool at the Beach House. Check with the Hilton Head site desk, as I'm not sure that Member Services is really up to speed with what's happening at HH. The HH onsite pool is warm enough so that kids seem to enjoy it mid-day, but I don't see much activity in the evenings. They also seem to do some maintenance at that time of year to have it done by Thanksgiving. Generally we have not found the food facility open at the Beach House and only limited hours at HH.
We generally walk the beach in long sleeve shirts, and enjoy the island in more sheltered areas in short sleeve shirts. It's nice on the room porches while the sun is up. Once the sun goes down it gets cool. The golfers seem very happy and the shopping is great, per my wife.
For us the drive from Michigan to HH in mid to late October is very enjoyable with the autumn colors. HH is very relaxing at that time, and not very full.