There's no requirement to wear a wetsuit while surfing, but you might want to for a number of reasons. First, if the sea is cold, it would be silly to surf in just a bathing suit. A wetsuit can help keep you warmer. If you're surfing in an area where the seafloor is rough or rocky, a wetsuit will help protect you from abrasions. What's more, some people get a rash on their torso from board wax, which can be prevented by wearing a wetsuit, even if it’s only a shortie.