Wetsuits are made of foam rubber, it is called wet because they do not protect you from contact with water and hypothermia (losing body temperature).

Surfing with wetsuits

    Water is able to pass wetsuits and get inside, creating an additional layer between your skin and the neoprene suit, meaning they can not keep heat inside your suit and keep your body warm. The colder the temperature - the thicker the wetsuit you will need. However, the thicker the wetsuit - the more it holds down your movements and the greater resistance you will face against water. 

    In addition, wet suit material is not breathable so your skin under the suit will have trouble giving out heat, and its main advantage -  heat retaining can play in the opposite direction and cause overheating in hot days or during intense activities.

    A wetsuit is good for surfing, kiting, diving, etc. where there is constant contact with water. Nevertheless, when it comes to sup, wearing a wetsuit is not your best option, because 99% of the time you will be standing or sitting on the board and work  your whole body, especially your upper limbs. Therefore your movements should not be constrained and your skin should be able to breathe and be in contact with fresh air so that excessive heat and sweat won't cause you any problem.