The Moon and the Earth have had a strange relationship for longer than we can understand. It has even been debated that, rather than a planet-moon relationship, it's really more of a double planet situation. Aside from that, given the Moon's dull grey, it somehow manages to appear in a range of colors while reflecting a very small amount of light.
The Moon reflects only 7% of the light it receives from the sun, and despite being flat, dull grey, the moon can appear pure white and extremely bright. The colour comes into play with the atmosphere. Because of the same light scattering principles involved in making the sky blue (the scattering and separation of the visible light spectrum leaving only blue), the moon can appear as red, orange, or yellow when rising because of how the atmosphere scatters the light.
The sun is also subject to this scattering, which, when lower in the sky, creates vivid reds, oranges, and yellows because blue light is scattered, and the remaining light is concentrated. Pollution can also cause the Moon to appear with colour. Smog, as prevalent in Los Angeles, can make not only the sky yellow, but the Moon as well.
All moons, stars and planets will appear red when lower in the sky because the eye will see them through greater portions of the atmosphere. Objects at the horizon are also farther away, and the angle at which their light enters the atmosphere supplying about three times as much atmospheric interference.
A lunar eclipse can certainly bring colour to the Moon through a similar principle. Lunar eclipses occur when the moon is opposite the sun, with the Earth in the middle. The darkness that encompasses the Moon is actually the Earth's shadow. Just before the Moon undergoes a total eclipse, it turns sanguine.
Regardless of how, our perception of the Moon is far from colourless. Despite its grey body, we witness the moon in a range of reds, oranges, yellows, even sometimes blue, though what we mostly see is white, but the important part is to remember that the Moon itself does not change colour.