I live in Tennessee and my favorite time to bike is the winter! (Mainly because summer is so insanely hot here) It's not uncommon to see 65 degree days in January and February, although you're more likely to be riding in 30-40 degree weather then. We usually get plenty of cold weather in March, and often times if it's going to snow here it will happen in March. Rarely more than an inch or two, but the problem is no one here knows how to handle snow. They may or may not have put salt on the streets, and of course no one can handle a car in snow/ice.

By late March, we usually start getting warmer weather. There will usually be a few chilly mornings here and there in April, but snow/ice/sleet is very unlikely by then. In May it actually starts to get hot, and after that I'd just try to be somewhere else if I were you, unless you enjoy a constant coating of sweat and insects.