The nice thing about Tennessee is that we have four distinct seasons. (Boy, did I grow to miss that when I lived in L.A. Even "perfect" weather eventually gets boring if you're used to the beauty of autumn and the weather actually "feeling" like Christmas.)
Middle Tennessee winters are usually pretty mild - rougher than what you have in Florida, but nothing compared to Northern winters. We usually get a small amount of snow; the ice is more of a problem. Many places don't have sufficient numbers of salt trucks to de-ice the streets after an ice storm since we don't get enough ice storms to warrant having them on hand, so when we DO get an ice storm, we're unprepared and everything shuts down. Kind of a Catch-22. Fortunately, they don't usually last very long, and the closer to an urban or suburban area you are, the better in this regard.
Spring is great with everything blooming and the temperatures usually very pleasant and mild.
Summer is very green, very HOT and very HUMID, although probably no worse and maybe not as bad as Florida summers.
Autumn, as I mentioned, is gorgeous with the fall foliage. September is still pretty warm, then it cools off nicely for October and November. It doesn't start to get really cold until well into December if not January - in my opinion, although I'm hot-natured.
Hopefully someone else can speak to your question about the adult communities in the Nashville area, I don't have any info on that. But there are a number of great golf courses around town - McCabe in West Nashville, Two Rivers, and The Legends Golf Course in Franklin to name a few.