I think it will depend on the variety of fig and the location in Florida. Florida has multiple different climate zones, mostly ranging from 8-10. I'm in 10b and basically on the line between sub-tropical & tropical (about 50 miles north of Miami). Here, I notice some slower growth during the winter months, but only a few of my trees actually lose their leaves. I've harvested figs as late as November/December and as early as February. I don't know if I've ever harvested in January, but only because I don't remember specifically.
This is a post I made this past November that only included a couple of fig pics, but you can see the LSU Purple still has all of it's leaves and a Cajun Gold with it's leaves still ripening figs:
http://figs4funforum.websitetoolbox.com/post/show_single_post?pid=1284954764&postcount=1
And, here's a post from the beginning of February showing several more with full foliage and ripe figs:
http://figs4funforum.websitetoolbox.com/post/show_single_post?pid=1286048546&postcount=1
I don't have a list of which ones go dormant, although, I do know the Strawberry Vertes and a couple of others will lose their leaves for a few weeks in Dec/Jan and then just put them right back on.