I don't know enough about the Georgia climate, but I think an unheated basement would get pretty cold. No AC might work, but I live in a state where nobody needs AC (plenty have it, but I think it's kind of stupid).

I would not finish a basement without HVAC. You need the heat in the winter to help the upstairs and the A/C will keep heat from rising into the rest of the house. The A/C will not run much, depending on how many windows you have.

Not true given time the cold will get in to the space. Now the AC may be avoided but the humidity can't so put in at least a dehumidifier.

I think I would improve the ventilation down there to control mold and the "musty" smell.

Not true at all, besement are the coldest and dampest place in the homes with cahnces of mold if there is not circulation.