We drove down from Montreal last December 29th. The weather was amazing for the drive down. My sister had left on December 26th and also had good weather for the drive down, however, for her return, she ran into that big storm that came from Texas and hit the southern states....Georgia, South and North Carolina, and Virginia. They had to drive through it all and she said it was awful. Coming from Quebec where this kind of snow is pretty standard from December to March, they were used to driving in it but the southerners had no idea what to do. Drivers were stopping in the middle of the highway (not even on the side), to scrape their windows with a credit card! Usually with no notice, just STOP! Thank goodness they had snow tires on so they were able to stop quickly. By the time we left to go home about a week later, there was none of that, not that it would have matter much because we took the Auto Train from Sanfor to Lorton. We were still surprised to see more snow in Viriginia than there was in upstate New York and Quebec.
Weatherwise, if you're going for the beaches, you are really taking your chances. You could have great weather BUT we were there the first week in January and had some really cold weather. One morning it was 39 F. My two older children called their Dad in TO who said it was 36 F there! I would go back to WDW again in January due to the lower attendance in the parks after the 1st or 2nd, but I wouldn't plan a trip to Florida hoping to spend time at the beaches, unless I was going further south, maybe as far as Miami. We actually stopped at a beach the day we got to Florida (my kids had never been to the ocean) and it was pretty chilly. The experience was nice, they picked up shells, skimmed some rocks, dipped their toes...but that was enough. Brrrr!
Overall, we had a fantastic trip in January and the only thing that could have made in better would have been warmer weather but like I said, as far as going to the parks is concerned, it's a GREAT time to go. Walking down New York St. on January 6th, with the Christmas carols playing and "snow" falling, continuing on to the Osbourne Family Lights did so much to rejuvenate my sagging, stressed out, exhausted Christmas spirit from the week before.
I guess that no matter what, you are taking your chances with the drive at any time in the winter months, but if you have any degree of flexibility (leaving a day early, etc.) I would take that chance.
Good luck!