Late winter into early spring is the ideal window in the Tampa area: before the summer flush and well ahead of the June to November hurricane season. Proper thinning removes interior and crossing limbs so wind passes through the canopy instead of pushing against it. Deadwood and genuine hazards come out whenever you find them, season regardless.
Why thinning works
A dense, unthinned crown is a sail. The point of a pre-season thin is to make the canopy porous so a gust moves through it rather than levering against the whole tree. Done properly the tree still looks full from the street; what has gone is interior clutter, crossing limbs and end weight on the long laterals. That last one matters most on big open-grown live oaks, where a sixty-foot limb fails under its own weight before the trunk ever does.
Why topping makes it worse
Hat-racking a tree back to bare poles is the most common thing done in the name of storm prep and it is actively harmful. A topped oak responds with a dense flush of fast, weakly attached shoots within two seasons. That regrowth is heavier, catches more wind and is far more likely to tear out than the structure it replaced. We do not top trees, and if a tree is genuinely too big for its spot the honest answer is removal and a better-suited replacement.
Where in Tampa Bay it matters most
Anywhere with open exposure to the water. Town 'n' Country, Apollo Beach and the bay-side neighbourhoods take sustained wind with very little in the way to break it, and the same species there loads up harder than it would inland. Plant City catches straight-line wind coming across from inland as well as the systems off the Gulf. Wesley Chapel's edge-of-subdivision pines are a category of their own, because a pine that spent forty years sheltered inside a stand does not cope with sudden full exposure.
Leave it too late?
Thinning during the season still helps, and clearing deadwood and hangers always helps. What you cannot do is thin a tree in the two days before a named storm arrives and expect much: fresh cuts and a crew working under pressure is not where you want to be. If a storm is inbound, secure loose items and call afterwards.