From Richard Barrans Jr., Ph.D.
"My understanding is that it is important for fog lights to be one color
(rather than white, which is all colors) because the different
wavelengths(colors) of visible light scatter off the fog droplets
differently. This phenomenon is known as "dispersion," because the
different colors of light in an image will separate from each other,
causing the image to "disperse." If you illuminate the road with only one
wavelength (color) of light, the images of the objects you see will still
become somewhat blurry because of the scattering of light by the fog, but
at least you won't have extra problems from dispersion. So, if we want to
use just one wavelength of light, which wavelength should we use? It turns
out that light with short wavelengths scatters more than light with long
wavelengths (short to long: violet, indigo, blue, green, yellow, orange,
red). So, a long wavelength light will be best. There's another thing to
consider, too: our eyes are not equally sensitive to all colors. It turns
out that we are most sensitive to yellow and green light. So, our best
compromise between sensitivity for our eyes and a long wavelength for least
scattering is yellow light."
This is one thought ... though others (with equally loft credentials) will dispute these thoughts.