I've got an astronomy background, so maybe I can approach this a little differently for people who aren't quite following where BB is going...

The sun produces what is, for all intents, white light.  The moon reflects the sun's light essentially equally across all wavelengths, so the light coming off of it is still considered "white" light.  (BTW, the moon is actually a very poor reflector of light--only about 9%.  Even though we see it as gray, it's really no brighter than freshly paved asphalt)

Now the light reaches the earth's atmosphere, where some of it is scattered.  However, blue light is scattered more than the longer wavelengths (a phenomenon known as "Rayleigh scattering").  The result is that some of the blue wavelengths coming from the moon are removed from the "direct" moonlight, and used to light the sky--it's why the sky is blue in daytime, and even a very dark blue during a full moon.

When you take some (not all, but some) of the blue light out of white, you get a slightly yellow cast to the light.

As the moon gets lower in the sky more light is absorbed, making the moon look yellow, and then orange once it's low enough that it begins to absorb noticeable amounts of green as well