Moonlight is simply the white light of the sun reflecting off the gray surface of the moon. There’s nothing in that interaction to give the light a bluish or greenish quality. In fact, scientific instruments have shown that the light from the moon is very slightly redder in color than direct sunlight.James Gurney
This article is fascinating and incredibly helpful. It answers the question of why artists tend to paint moonlight as bluish or greenish. Another one to add to my nocturne resources.