Simple test for you: Get your fingers slightly damp, reach into the freezer and grab a piece of ice. Do not remove it from the freezer. After a few seconds, try to let that ice go. If you did this correctly, the ice will at least partially adhere to you fingers. It won't slip around like a greased pig or turn into a big puddle of water, but it will stay dry and solid until you bring it out into warmer temperatures. The reason it sticks is because the water on your fingers is now frozen with the ice, and even though it was wet before, once it freezes it becomes as dry as the ice.
So the answer to you question is no, ice is not wet. Water is wet, and melting ice becomes water, but the ice itself is not wet(unless there is water on it).
So the answer to you question is no, ice is not wet. Water is wet, and melting ice becomes water, but the ice itself is not wet(unless there is water on it).