Cold weather actually appears to stimulate the immune system.I'm neither a doctor nor do I play one on tv, but I've been led to believe that being wet and cold can make you' more susceptible to developing a cold if you are exposed to germs. And we are always exposed to germs.
That said, cold for Florida ain't cold!
The reason we tend to get sick more often during cold weather is we stay inside with other people making spreading germs/viruses much easier. Also the dry heat produced by heaters dries out the mucus membranes reducing their ability to fight off foreign invaders.