Old European farming lore connects heavy dew with a bright moon, and the connection holds for exactly the same reason the frost one does.

Dew forms when the ground cools below the dew point, and it cools fastest under a clear sky. Moonlight is the marker of clear air, not the cause of the water. The lore also holds that dew gathered by moonlight is medicinal, which is a separate claim and not one anybody has managed to support.