I agree with above posts on gray tank dumping in any season. If you are in southern Fl. you will probably not have freezing issues even if you leave the gray tank valve open. You probably do not need the tank heaters.
You may have tank or pad deterioration due to high spot temperatures with an empty tank. See instructions for your pads. You are likely to have gray water freezing issues if you do not close the valve until significant dump can be achieved.
Water flowing through the gray tank will probably not freeze. Water trickling through the stinky slinky may freeze and block the drain. How low the temp is and how long it stays low matters. There may be no place in FL that would stay cold enough for long enough to cause grief. You probably do not need tank heaters.
In Wisconsin where I live, I fill the fresh tank, disconnect "city water" line, remove the stinky slinky, and turn on the tank heaters when liquid has accumulated. I also drive to a dump site far away because most dump sites are closed in winter and most campsites do not have sewer hookups.
Freeze ups damage campground plumbing unless winterized just like my TT.
I wish you good luck and happy trails ahead!