This is similar to the colors we see during a sunset.
The moon is actually emitting all different visible colors which combine to make white. As the moon is overhead we are able to see a white moon, but a lower moon position make the moon's light travel through more of the atmosphere. Colors with shorter wavelengths are scattered in the atmosphere, which is why we end up seeing red, yellow, and orange colors remaining. Particles in the atmosphere, including dust, can help scatter the light.
A sunset is similar to this because the sun's light rays must travel through more of the atmosphere as the sun's begins to set. So we see orange and red colors.