We spent a couple of days golfing, one day was taken up with a beach horse ride, a guided nature walk, a few sessions round the pool , visit to the Premium outlet mall, a sunset dolphin cruise, a walk along the beach and a few visits to some of the other stores in the area. The aren't really any "whole day" things to do at HH but a lot of halfday activities. It gave us the opportunity to have a relaxed time and not have to rush anywhere. We also took an hour or so going round the local art gallery that has a lot of Wyland paintings ( there is a similar gallery at the BW in Orlando). If you don't know Wyland is a well known wildlife (mostly marinelife) artist.
The weather was a bit of a mixed bag. First 3 days it was in the high 70s (was nice pool weather) next 3 days was low 70s (ok pool weather) last 3 days was in the mid 60s ( hot tub was real nice, pool was heated so it was ok in the water, but chilly when you got out). This was in December, but I think the weather can be variable pretty much anytime from November to March. It's usually ok, but you can get a cold snap at any time.
HH does offer some good kids programs, there are also some nice adult ones. We spent a nice evening at a wine and cheese tasting (while DD went on a pizza and movie evening that the
DVC organised) . Chef Gordon does a number of food and beverage evenings and they are well worth attending, if the kids are of an age that allows them to be entertained by the kids activities. Best event of the vacation was "A private affair" which is a meal cooked by Chef Gordon of the DVC just for your group. This is now done at the Beachhouse, but when we attended it was in a 3 bedroom grand villa showhouse used for DVC presentations. Wonderful food, plenty of wine and he's a very entertaining and informative host about DVC and the HH area.