The colors of most things don't appear to change when you move from sunlight to fluorescent light to incandescent light to firelight, even though the actual ratios of wavelengths that are hitting your retina are quite different. This is because your eye automatically adjusts colors based on the ambient light. 

So the perceived color of the moon depends on a combination of physics and neuroscience. See [this question](https://biology.stackexchange.com/questions/40358/why-doesnt-the-ambient-lighting-condition-change-the-perception-of-colors-we-se) in biology.stackexchange.