Your shotgun will have to be unloaded while in the park. I hope the following helps:
State parks, historic sites, and recreational areas: Except for those with a valid license to carry, it is against the law in Georgia to carry or attempt to carry a deadly weapon onto a park, historic site, or recreational area. The term 'park, historic site, or recreational area' means a park, historic site, or recreational area which is operated by or for and is under the custody and control of the Department of Natural Resources (DNR). Without a valid license to carry it is unlawful for any person to use or possess in any park, historic site, or recreational area any firearms (with a GFL it is also legal to carry that firearm into buildings on the property). It is unlawful to carry onto park, historic site or recreational area property, bows and arrows, spring guns, air rifles, slingshots, or any other device which discharges projectiles by any means (unless it is a pistol, revolver, or concealable firearm and you have a GFL), unless the device is unloaded and stored so as not to be readily accessible or unless such use has been approved within restricted areas by prior written permission of the commissioner of natural resources or his authorized representative. It shall be unlawful to refuse to leave a park, historic site, or recreational area after violating any law or regulation of the Board of Natural Resources promulgated pursuant to Code Section 12-3-9 and after being directed to leave by an authorized representative of the department. (If you are caught carrying a firearm without a license or breaking any of the other rules, then you can be asked to leave the park area by an authorized rep from DNR.) Any person who violates any of the provisions of this Code section commits the offense of criminal trespass. (If you refuse to leave after being asked too, then you can be arrested for criminal trespass) (12-3-10, 16-11-127)