We're just north of NYC and have been driving down to Fl for about 10 years with 4 children. We've done this trip about 15 times. For us it is a cost saver as well as a convenience. I don't have to deal with the hassles of flying as well as we can bring what we want. (When the children were smaller, that meant that if a special toy had to come, that it was easy to say yes, now its all the electronic devices that teenagers can't leave home.)
The weather can be an issue during any season. Summer we have hit hurricanes and tropical storms. We were once forced to spend the night in
Georgia. The winter has the north storms. NY may be clear but DC had ice and snow. Then many trips were smooth sailing with no problems.
You have to be flexible and realize your limitations. We never plan to stop and drive straight to Disney. Our best drive time was 18hrs our worst 26. My husband likes to drive and when he is tired, I will drive. I couldn't do the drive like he does. The times that have been traffic free have been when we left before 1pm or at 1am. The kids are troopers and realize that we won't get to Disney until tomorrow. No one asks how long until tomorrow hits, usually the youngest.
I like to drive because we can leave home when we want, go anywhere we want because we have the car when we are in Florida, (we even drive to the parks because that is even quicker), and if we want to stay an extra day, it is doable.
You just have to be prepared and I never have let it bring down the trip that the drive home is tough. No more adrenaline, looking forward, everyone is tired and not looking forward to the long drive home. I always tell my husband that we should consider staying over midway to break up the drive home but he always seems "happy" to be going home (he is not a disney fanatic like I am, just a good sport.)
You just have to know what you are getting into. Flying is nice and quick. They both have their pros and cons.