I want to add that that range map is highly speculative.
I have seen two cottonmouths in the Atlanta area, 100% positive ID. This was 50 years ago. One went to snake heaven after trying for several minutes to bite someone from a brush pile. No question about the fangs, mouth, and post mortem snake ID.
There also have been reliable reports of cottonmouths in Wilkes County. There is no reason they can't come on up the Savannah River, and multiply in the various lakes which provide massive heat sinks against winters,
If you try to pin a DNR biologist down on how that map is made, they admit it's their "best guess."