Florida did have slaves just like the rest of the South. While Florida's inhabitable climate and winter only culture might have hampered this a little, Florida did still fight with the Confederacy in the Civil War and enact black codes, segregation, and other racial prejudices. Florida was slow to desegregate, although it did occur a bit quicker in Florida than in the main "Deep South" states such as Georgia.
Now Florida's racial diversity goes far beyond black and white. Florida's geographic location makes it a safe haven or immigration destination for many Hispanic people. South Florida in particular (and Miami especially) has been completely transformed by its Hispanic population. Spanish is the only language of many living there. Policy, culture, business, and society are all affected by this demographic. The Hispanic population holds a lot of weight (after all, the might up quite a chunk of the voting population). You can truly understand Florida without considering its Hispanic populations. The vibrant Hispanic culture, with its food, language, and music, transformed places like Miami and Ft Lauderdale and can't be ignored.
Of course, the original Floridian race, the Seminole Indians, can not be forgotten. They still have a rich and vibrant culture in South Florida. They make money from their casinos and hotels as well as their cultural attractions such as alligator wrestling and hand made crafts. While they might not be as widespread and visible a group as the Hispanic populations, they have deep and lasting roots in Florida.