Our church youth group does a spring trip every year to Chickasaw State Park in Henderson. It is on Hwy 100. That is going towards Jackson, Tennessee.There are a few state parks up that way beyond Millington. My husband and I just live about 10 minutes south of Millington. Chickasaw State Park has air conditioning in all cabins. They have group lodges also. Not sure about them but I think they would be air conditioned also. Would be interested in knowing where they went. We are going to Chickasaw State Park the end of August and staying in a cabin for 3 nights. You can go horseback riding, rent rowboats and dreamboats on Lake Placid, they have a nice restaurant also. This is a link to Chickasaw, it is 18 miles south of Jackson, Tn.
http://tennessee.gov/environment/parks/Chickasaw/
Group Lodge
This facility accommodates 40 persons. The building features divided quarters with bunk beds and sleeps 20 people to a room. Central heat and air are provided as well as dishes, utensils, microwave, ice maker, freezers, refrigerator and stove. Groups must supply their own linens.