It is really difficult to say when is the best time to move to Tampa. If you have a choice and have the choice, winter may be your best option. Even though the busiest time of year for moving is summer, winter may be a better choice. This is especially true if you are coming from the chilly north. Why wait until spring or summer to move? Why spend one more year freezing over the winter? There are not many good reasons for that!
But, if you are a local, why move during the winter? It is easier to get movers on the days you want. During the summer, the best movers are booked out solid, sometimes for weeks! The slow moving season is during the winter, so you can more easily set the schedule and get a quality moving company to move your family.
If you are moving locally in the Tampa Bay Area, winter is also a good choice. You can avoid all the work in the hot steamy summer, you can find a good moving company, and probably get better prices on the move. While winter is the tourist season, it is not the moving season. For stressful events like moving, you can minimize the stress and pressure by moving during the off season.