I was in HHI Presidents Week (3rd week of Feb) in 2002. We usually go the 2nd or 3rd week of April when the PGA tournament is in town. It was VERY quiet in Feb. I felt like a local. Many of the more tourist type restaurants were not open or only started to open with limited service at the end of the week (ie. Salty Dog Cafe) There are many restaurants that are still open year round though-you shouldn't have a problem finding places to dine.
The weather was sunny but, cool- I think like 60's maybe low 70's. I wore a lot of layers (long sleeve shirts, sweatshirts) and not a lot of shorts. For me, though, 60's or 70's with lots of sun comming from a middle of Feb. Central New York winter was a really nice break for me. Didn't do a lot of swimming or laying on the beach or by the pool-although our pool was heated and I could have if I wanted to. We did a lot of bike riding, walking, and shopping. We went down to Savannah, GA for the day and took the tour and walked around.
Have fun! We'll be there again this year the 3rd week of April (year #8)