They were permanent residents, whether you're talking about the 16th Century or later. Also, for many centuries prior, if not for the entirety of human history in Florida (there's no archaeological evidence that would indicate that ancient Floridians were making long-distance annual migrations en masse). In this post, I discussed three of the major nations in Florida in the 16-17th Centuries - the Calusa, the Timucua, and the Apalachee. That post is mainly about their governments, subsistence, and a bit of their history. You're probably more interested in their housing and their clothing, right?

For the Calusa, a basic outfit consisted of a breechclout of woven palm fronds for men and a skirt of palm fronds or Spanish moss for women. Those distinguished by rank or accomplishment might also wear feather or pantherskin cloaks. Their houses ranged from small open-air chickee to large enclosed elite houses (that looked something like this. Considering that image depicts a house with windows (not glass windows though), it's based on the description of the certepe's house, which was said to be able to hold 2000 people during a council). As for the chickee, it's a type of building still in use in southern Florida (though usually with some modern embellishments). This illustration shows you a basic chickee. A typical chickee home will consist of cluster of a few of these, each with their own purpose (one for sleeping, one for cooking, one for storage, etc). The thatching usually comes down further, but I went with this illustration so you could see what the "inside" looks like better. Chickee were adopted by the Seminole as they moved into southern Florida, and have been known to withstand hurricanes.

For the Timucua and the Apalachee in northern Florida, basic attire was similar to the Calusa but they used deerskins, variously decorated with paint or shells, rather than palm. Woven Spanish moss was still popular with women among the Timucua however. Common Apalachee and Timucua houses were circular thatch buildings, as seen in this illustration. This is a recurring architectural pattern for northern Florida, that gets scaled up for larger buildings like this Apalachee council house (a reconstruction of a 17th-Century building).

Hopefully that answers at least some of your question. If I've missed the mark on your intent, let me know and I'll abut trying again.