I guess it all depends on your definition of cold. I had a roommate from Freeport, Bahamas in college and she had winter clothing. When I saw here pull out a fluffy winter coat, in Tampa Fl, I just about fell to the ground laughing. But being from Wisconsin I have a whole different definition of cold then she did.
The water will most definately be brisk when you first enter but as long as you aren't expecting bathwater temperature you should be fine.