Most regional theme parks close during the winter or for part of the winter. The only parks that are open year round are the parks in California and and Florida. Florida would probally be the best choice for you. Some parks include Disney, Universal Studios, Universal Studios Islands of Adventure, Busch Gardens Tampa, and Boomers at Ft Lauderdale, and Old Town at Kissammee, which I believe is near Orlando.
Stone Mountain Park, Georgia is also open.
Hope that helped. :]