We have been to (and enjoyed) HH many times during cooler months. While a lot of the "usual" activities may be outdoor weather related there are many options even during bad weather with galleries, museums and boutique shops to explore.
You can take a trip into nearby Bluffton's Old Town for some history, go to the Coastal Discovery Museum on Hilton Head. The Arts Center of Coastal Carolina (within walking distance of the resort) offers broadway production shows throughout the year as well as a number of smaller productions and there are exhibits of local culture in the gallery at the center. The Broadway productions are very good with lead roles filled by Actors Equity performers and local residents filling in the chorus roles. "9 to 5" is playing soon.
A day trip into Savannah (45 minutes away) or Charleston (2 hours) can offer nice options if the weather is not conducive for a Dolphin Watch tour, kayaking, paddle boarding, parasailing, crabbing or fishing (which can all be done right from the resort or the Shelter Cove Marina). HH has miles and miles (and miles) of paved bike trails all over the island and it is fun to explore the area by bike. Down in Sea Pines (minimal auto pass charge) you can visit the lighthouse, more galleries, tour the ruins of the old Stoney - Baynard plantation (this can be done by bike too), visit the oyster mounds in the Lawton area (another bike option), check out the Salty Dog Cafe - all within Sea Pines. In addition, golf and/or tennis is readily available at the many venues available all over the island. Near the resort are a couple of mini-golf courses and there are also theaters within a couple of miles.
The resort itself offers a wide variety of recreational activities for all ages so be sure to check out the activities list when you arrive.
One over looked activity often missed with all of the other options is ... just relaxing with a good book in your villa or in Big Murgies Den (also check out the old photos in the Den as there are some recognizable people in some of those). Ask the front desk for a list of Hidden Mickeys to look for around the resort - there are many along with reference to past and current Disney characters (both animated and real).
Here is a list of
101 things to do at Hilton Head.
We have been at the resort in January/February when highs were in the 40s and times when the highs have been near 80 - and that can change from one day to the next (so be prepared!). Reservations at HH during the cooler months are readily available at 7 months and point costs are a real bargain compared to summer.
Have a great stay.