FLL airport authorities have announced officially closing the airport at 1030am local Thursday Oct 6th.
Southwest's web page/travel advisory isn't quite that specific yet, although a cursory check around noon today (Wednesday) indicated that all flights for Thursday/Friday/Saturday into/out of <at least> FLL & PBI were sold/blocked/cancelled/held.
The FAA has already posted the FLL closure for tomorrow; presumably more to come following the early morning planning conference between the FAA Command Center, the local/impacted FAA facilities and the airlines.
NATIONAL AIRSPACE SYSTEM STATUS
Last updated Thu, 06 Oct 2016 03:13:03 UTC.
(Provided by the FAA's Air Traffic Control System Command Center.