Well that depends really... wood, foam, what part of Carolina, Coastal or Mountain? How sealed up is the shop?
First off I wouldn't put my batteries out there. The worst thing would be extreme changes in temps on balsa as it will expand and contract and make weak joints and such.
It's not going to kill them though. I have some stuff I leave in my camper year round and see no ill effects from them. Our temps are fairly moderate here in the Tidewater area of Virginia also, not to different from where you are probably.