That was a long time ago, and in fact, it was kind of like that across the state. Read "Miles From Nowhere" by Barbara Savage. Notice how they were doing all right cycling across the entire US until they got into Florida, and how things really got bad for them in the Keys. I can concur on their perceptions of the Keys and on Florida in general. After all, I was born and raised here, and I have cycled across the state many times, including down in the Keys. That was the past. it has changed.
Certainly you will encounter more traffic in winter, and higher prices. State campgrounds are your best bet, and you might need reservations unless they are on a first-come first-served basis.
Do not be worried about safe cycling. The roads provide plenty or room. Motorists are very reasonable. There are plenty of cyclable sidewalks. There is one long dedicated bike path. It is actually very good for cycling. No problem. Of course, people being what they are, it is possible to have an encounter with a very irate or unreasonable person driving a motor vehicle. However, that can happen anywhere, any time. The big things about the many bridges is they expose you fully to winds. I do not remember having trouble with traffic on any of the bridges.