Merriam-Webster's definition of wet is
"consisting of, containing, covered with, or soaked with liquid (such as water)"
Water consists of liquid and matches the description of "such as water." Therefore, water is, by definition, wet.
The internet has not accepted this conclusion and have countered with two lines of reasoning:
However, anyone who has taken chemistry should know that groups of molecules of water define the difference between ice, water, and steam.