The answer would depend on the state in which you currently are in. Laws vary from state to state and there is a huge variation in rules governing handgun hunting.
Iowa recently joined those states permitting handgun hunting. Every state has a department of fish and game which defines teh rules regarding possession of guns for hunting purposes.
You will also require a hunting license (or even a permit) to hunt deer and turkey which again depends on state laws.
In Georgia, to carry a handgun openly or concealed (outside of your home, your car, or your business), you must have a Georgia Firearm License issued and the concealed handgun must be carried in any type of holster or any other securing device . While, 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
Possession of handguns in New York State requires a NYS Pistol Permit. New York does not recognize permits issued by other states. This too can be use during the regular deer season or early and regular bear seasons.
I would suggest you to visit the your Fish and Game department depending on your state, and you will get all information that you require.
I hope this helps.