Hi Susan, what do you want to grow? In winter we are considered "subtropical" since we do get some cold nights in the fall/winter/spring. I'm just north of you in Sarasota, and already last week we got down to 50deg.
So the short answer to "when is the growing season" is "All year" because there are things that will grow here all year. But if you want to grow things that like cool nights, then NOW is the time to plant because they will do great until about April when it starts to get warm enough that you have your a/c running day and night. i.e. the nights lows are above 70 or so. Annual flowers from seed such as marigolds, nasturtiums, pansies etc. will give you lots of nice color through the cool weather. Cool season veggies like salad greens, broccoli (and other cabbage-y things) carrots, beets etc. also need cool nights. Plant them now, now now! (there are good transplants available at the garden centers, generally)
Starting in late February, you will be able to plant everything you'd normally plant "up north" in May to grow through the summer. If you want certain varieties of tomatoes or peppers, though, buy the seeds now, and start them from seed in late December or January so they'll be big, lusty transplants by late Feb. Btw, tomatoes generally do not like the hot weather here in summer, that is most varieties simply won't set fruit after the night temperatures get above 75deg. The plants get really sad, flowers fall off, etc. Peppers, eggplant, basil and the like do love our hot humid summers though. But plan on your tomatoes failing in late May or early June.
If you're ambitious you can grow the warm season things through the winter, just plan on covering the plants with frost cloth on any nights that get below 50 or so. Make a tent, to trap the warmth rising from the ground for them. Oh, and don't use plastic! It does more harm than good. I harvested tomatoes and peppers from December all the way through May last year and only had to cover them maybe 5 nights.
One more thing, if you are planning to plant in the ground, our soil is generally just grey sand so it needs a TON of amendments to support growing vegetables. Other plants not nearly so critical, but you won't get much production from your vegetables if you don't add tons of organic material. The landfills here make excellent compost and it's free for the taking (but you have to load and transport it yourself).
