Here, in the Tampa Bay area, the answer is most likely, no. While the cooler weather is nice, it doesn't get cold enough, long enough to really affect your tennis equipment.
If it got cold enough (like up north), stringing your racket a little looser can help reduce the shock of impact. Around here, you won't have to change anything.
One thing to keep in mind, even though it is cooler in the fall and winter, you still don't want to leave your rackets in the car all day. It can still get hot enough in a car to potentially affect both your rackets and strings. Keeping them inside a climate-controlled building or house will keep your racket and strings playing better longer.
