One of my favorite vacations that my husband and I took as a newly married couple was to stop for a weekend at Callaway Gardens on our way back from the coast. It is such a lovely place, and they have such excellent staff. I was happy to see the following information on Southern Savers site:
“Beginning January 1 through February 28, 2010, Callaway Gardens is inviting everyone to “Be Our Guest.” Admission is complimentary for these two months providing guests with the opportunity to enjoy time with their family and friends reconnecting in nature. Just show up - no ticket necessary to enter the Gardens.” - callawaygardens.com Callaway Gardens is south of Atlanta near LaGrange GA.
You might want to check out their website to see what might be available for family activities during the winter before you plan your trip. I would think that most of their gardens would not be at peak until later into Spring. As I remember there are many walking trails and hikes on their property and the surrounding area.