First, the Cottonmouth's range doesn't cover the entire state of Georgia. It isn't found in mountainous areas of the north because the habitat isn't suitable and winter conditions are too severe. Second, many - in fact, most - locations within its range don't offer suitable habitat, either naturally or anthropogenically.
The distinction between range and habitat is a tricky one that is really a matter of scale. No species occurs ubiquitously across a landscape, only where suitable habitat occurs. Some species have narrower habitat requirements than others. So, if a species is out of its habitat, is it also out of its range? The answer is arbitrary and depends on the level of precision desired and possible. Look at range maps in different field guides and you'll quickly see that species' ranges are mapped very differently and that newer books tend to be more precise; the trend is towards mapping of suitable habitat.
Locust Grove is barely within the Cottonmouth's range, broadly defined. I'm not familiar with the area but if there are no Cottonmouths there it's because there's no suitable habitat (left?) or because the species has been extirpated by means other than habitat destruction. Cottonmouths are not exactly the most popular species around. One also must consider that species usually occur at low densities at the edges of their ranges because conditions there are marginal for them.