It has been a long time since I lived there per se, but as far south as Tampa/Orlando can get some real cold snaps. It's not common, but I've been there twice in Dec/Jan when they had the salamanders going and they were spraying the fruit trees with water to isolate them from freezing temps. I remember being at Epcot one day with a down coat and almost no one in the park because it never got above 40 and it was windy/rainy.
Like I said, not common, and certainly not MN, but it can get "seasonal" down there.
As far as Hurricanes, I only lived through one down there in Miami. It was Andrew I think. I remember it hit the tip of FL, but that meant the onshore surge was impressive to say the least. The state is so skinny that you can get some pretty serious effects from hurricanes, but gulf shore does have the protection of some land between you and the worst of most hurricanes. My grandparents lost a roof on their modular in Ruskin (just south of Tampa) in that storm.
I think the worst part about FL and hurricanes is if you decide to leave. You have a choice of only three highways. Just getting from Miami to Jacksonville during Irma took me two days, and no chance of a motel, you're sleeping in your car. Should have just stayed in Miami because it ended up hitting Naples. I would say, pick a spot that doesn't get bad winds, ride out the tide surge, and stay put. Trying to leave FL during a hurricane can be pointless. At least if you stay home, you have your belongings in a hurricane-resistant building instead of two pairs of underwear and beef jerky in your easily-crushed-by-a-palm-tree Camry.
I very much enjoy Tampa/St Pete. Plenty of retirees in that area so you won't be flooded with spring break kids, and as far as I know the crime rate is pretty low. Only a couple hours from Orlando and not so far down the peninsula that it takes forever to get back to the "continent." I never spent much time in Naples because I can't even afford a beer there. Miami is everything I should love on paper, but do a search for the Miami thread from last month. I personally prefer the northern half of FL more than the southern half if I were to live there.
Personal preference here in case you happen to be fisherpeople... if I'm going to live on the water, I prefer ocean to gulf. One of the reasons I left FL (other than hating Miami) was because the ocean side was bloody expensive and that's the side that gets storms with names attached to them, but the gulf coast (while being lovely) just has smelly salt water, but very little of the beach/ocean feeling. The bay is approachable for smaller boats and has some interesting fishing, but you have to go a LONG way out to get more than 20' deep, so it does limit the larger species, and by the time you get far enough out in the bay to fish for fun things, you need a boat that is just as big as what you would need for the Atlantic side anyway. The gulf has an interesting biome. The clockwise current brings the MS delta sediment along the panhandle and dumps it on the FL gulf coast (hence why it's so shallow) which also makes it a bit lower salinity. It's one of the reasons that Manatees love it there, but also one of the reasons why many fish species don't prefer it.