I have a friend in Stone Mountain- they got snow last year, fell under the "freak of nature" category.
As said, Stone Mountain Park does have a day where they make snow. (And it's "real snow", not sure what fake snow would be.

They make it with a snowmaking machine, same as what our ski areas do to augment Mother Nature on the slopes.) My friend had paid for her kids to do that a couple years ago. She pointed out it was actually good- just enough snow to play in, but not enough necessitating full blown snow gear like a long weekend would. (She layered the kids' clothes and put them in their rain boots w/ extra socks.
FYI while there are different types of snow (powdery, more like fine sugar, and then sticky, the kind you can compacts to make snowballs, etc- and 100 variations in between), it has to do with temperature vs just first/last snow of the year. We can make snowmen in January and have had powdery blizzards in April. Depends on how warm it is.