I think Tallahassee may even be a bit cooler then Jacksonville during the Winter months. My perspective is from someone who moved down from Maryland, however, so it may be quite different from someone moving UP from Miami.
Yes, it does get chilly in the Winter months. Maybe a half dozen nights a year will get below the freezing mark. But it's a rare day that does not reach at least 50 degrees. For me, this is just fine. But you won't need to buy a snow shovel, if that is what you are thinking.....