As is generally known, the moonlight is actually sunlight reflecting from the surface of the Moon and reaching us here on Earth. You ask yourself the question, whether the moonlight may have a different colour than the sunlight, especially since a nightly scenery usually appears to be bluish. Also movie scenes, are portrayed in blue and so are many pictures and photographs. We would like to forestall the answer: the moonlight is nearly white. The night appears blue due to other reasons.
On the one hand, there is the twilight – which is also referred to as »blue hour« – that lets us experience the beginning and the end of the night in blue, and hence establishes the colour blue firmly in our consciousness. Therefore, this is the colour in our mind. By the way, the bluish twilight is caused by the ozone layer of the atmosphere.
On the other hand, the sensory cells inside the eye that are responsible for colour perception (so-called cones), are kind of put to sleep due to the approaching darkness, while the cells that enable the brightness perception (so-called rods) are activated more. Because the rods mainly react to blue light, the perception of this colour spectrum is enhanced at night. This is called the Purkinje effect, named by a Czech anatomist Jan Evangelista Purkyně.
So, the blue light of the night is only blue from our perception. The moonlight has no part in this. However, if people might feel blue at night, this could possibly have other reasons …