An object the mass of our Moon is too small to hold onto a significant atmosphere. Even if it did have liquid water, it would just boil off because water boils in a vacuum. Generally speaking, the closer to the star, the less likely you'll find an object with a significant portion of water on it, whether solid, liquid, or gas. The stellar winds are capable of breaking apart oxygen from hydrogen in a water molecule and blasting it off into space. This is why most moons and bodies at Jupiter and beyond contain a fair amount of water since the solar wind isn't as strong at that great distance.