Why can Devil Fruit users use their abilities while wet?
TL;DR 


Kuzan freezes the water without touching it. So the water doesn't nullify him. Think like how Ace tries to vaporize sea water with fire. He only creates those fire he isn't the fire in that case.
Sea water doesn't cancel Devil Fruit powers it only weakens it for the Paramecia type.




From Wikia article on Kuzan:


  In addition, Kuzan is one of the few Devil Fruit users who has adapted
  their powers to travel efficiently across the sea. In his case,
  freezes the water underneath Ao Chari then rides across the sea, due
  to the water freezing as the wheels pass over it. This freezing
  ability, which can be used on a very large scale, renders Kuzan one of
  the few Devil Fruit users who can actually counteract the weakness of
  falling into a large body of water and drowning, as he can just freeze
  the water and stand on the ice.


From the Wikia article on Logia


  Logia Devil Fruits allow a person to create, control, and transform
  into a natural element or force of nature, depending on the fruit. The
  user can transform partly, or completely.




For Luffy's case, check this post.