Paging Kyle Harris. Pick up the white courtesy phone, please!
I'm pretty confident in saying many, if not most, of the courses stay open around Tampa during the summer.
And the drive from TPA to World Woods is not bad at all. With no traffic I think it is about 1 h, maybe a few minutes more. And, BTW, I simply love WW. Been there probably 10 times now for spring break trips over the past 15 years.