Yes, even in Florida, hypothermia happens. It's possible to hike the Florida Trail in February and wake to frost on the tent and water bottles frozen, in Big Cypress Swamp as well as Eglin Air Force Base.

The risk increases substantially when you wade through swamps or stream crossings in chilly weather, but can also happen on a warm spring day when temperatures plummet at night and you don’t have a warm sleeping bag with you. Don’t assume just because it’s Florida that a 40°F sleeping bag (or none at all) will be adequate protection. During prime hiking season – the winter months – a 20°F bag should provide reasonable warmth. I’ve carried a 0°F bag and been glad I had it. Be aware of the weather around you; don’t let your gear or clothes get wet on a cold day if you can help it. Carry hand warmers and energy bars in your pack.

Signs of hypothermia include shivering, difficulty thinking, slurred speech, confusion, and sleepiness. If you’re in wet clothes, immediately change to something dry. If you’re with companions (or you notice a companion suffering from any of these symptoms), do whatever’s necessary to bring the victim’s core temperature up, from feeding them hot liquids to diving into a sleeping bag with them.