Depending on what your personal wants may be, there is still of lot to do in January at HH. Weather will range from 40's to 70's - so swimming (in the heated pool) will still be an option. The beach will still be there - even if the ocean is too cool to swim - so long walks are a very good option. There are miles of bike trails and the beach sand is great too for bike rides. Golf and tennis can be enjoyed throughout the year.
There are lots of dining options and many of the shops, boutiques and outlet stores are open thru the winter. There are many galleries on the island to enjoy as well as museums and historical locations. Horseback rides are also available at nearby Lawton Stables at Sea Pines.
Many of the water related activities can still be enjoyed - fishing, shelling, nature walks, crabbing, Dolphin tours and canoeing can all be arranged thru the recreational staff at the resort.
One other activity very important both at HH and at the resort in particular (and very often overlooked by many) is relaxing. I tend to enjoy taking a book, sitting on the balcony and trying to read while watching the osprey, dolphin, manatee and sea otters in the marsh - unless I doze off first.
Have a great trip - I know you'll find plenty to fill your days.