Being a liquid, water is not itself wet, but can make other solid materials wet.
Wetness is the ability of a liquid to adhere to the surface of a solid, so when we say that something is wet, we mean that the liquid is sticking to the surface of a material.
Whether an object is wet or dry depends on a balance between cohesive and adhesive forces. Cohesive forces are attractive forces within the liquid that cause the molecules in the liquid to prefer to stick together. Cohesive forces are also responsible for surface tension. If the cohesive forces are very strong, then the liquid molecules really like to stay close together and they won't spread out on the surface of an object very much. On the contrary, adhesive forces are the attractive forces between the liquid and the surface of the material. If the adhesive forces are strong, then the liquid will try and spread out onto the surface as much as possible. So how wet a surface is depends on the balance between these two forces. If the adhesive forces (liquid-solid) are bigger than the cohesive forces (liquid-liquid), we say the material becomes wet, and the liquid tends to spread out to maximize contact with the surface. On the other hand, if the adhesive forces (liquid-solid) are smaller than the cohesive forces (liquid-liquid), we say the material is dry, and the liquid tends to bead-up into a spherical drop and tries to minimize the contact with the surface.
Water actually has pretty high cohesive forces due to hydrogen bonding, and so is not as good at wetting surfaces as some liquids such as acetone or alcohols. However, water does wet certain surfaces like glass for example. Adding detergents can make water better at wetting by lowering the cohesive forces . Water resistant materials such as Gore-tex fabric is made of material that is hydrophobic (water repellent) and so the cohesive forces within the water (liquid-liquid) are much stronger than the adhesive force (liquid-solid) and water tends to bead-up on the outside of the material and you stay dry.
Though, you could also answer:
If we define "wet" as the condition of a liquid sticking to a solid surface, such as water wetting our skin, then we cannot say that water is wet by itself, because it takes a liquid AND a solid to define the term "wet."
If we define "wet" as a sensation that we get when a liquid comes in contact with us, then yes, water is wet to us.
If we define "wet" as "made of liquid or moisture", then water is definitely wet because it is made of liquid, and in this sense, all liquids are wet because they are all made of liquids. I think that this is a case of a word being useful only in appropriate contexts.
So, depends how you define things. Btw blood orange season is coming to it's end