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Water isn't really wet because "wet" is defined as a liquid sticking to other surfaces. If you have a melting ice cube, the ice itself is wet because it has water on its surface. However, if the ice cube is frozen well under 0C/32F, it's dry because the water isn't a liquid and therefore can't stick to the ice cube. When you ask if water vapor is wet, the answer would be no. Liquid water can't stick to water vapor.
tl;dr: There's no liquid water on water vapor, so it isn't wet.