A valid firearms license is required for legal carry in GA. If the river is located on Army Corps of Engineers land, then all carry is prohibited.
Otherwise, state parks, WMAs and local parks are all good to go for carry.
Here is the best rundown of GA gun laws: http://www.georgiapacking.org/law.php
You are right about the Corp of Engineers, however:
O.C.G.A. § 16-11-128
Carrying pistol without license
(a)A person commits the offense of carrying a pistol without a license when he has or carries on or about his person, outside of his home, motor vehicle, or place of business, any pistol or revolver without having on his person a valid license issued by the judge of the probate court of the county in which he resides, provided that no permit shall be required for persons with a valid hunting or fishing license on their person or for persons not required by law to have hunting licenses who are engaged in legal hunting, fishing, or sport shooting when the persons have the permission of the owner of the land on which the activities are being conducted
; provided, further, that the pistol or revolver, whenever loaded, shall be carried only in an open and fully exposed manner.