Answer:  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. Now, I don't know what kind of light bulbs are used in fog lights, but another consideration used in street lighting is cost and efficiency.  You may have seen some yellow street lighting in some places; this is "low-pressure sodium vapor" lighting.  The special thing about this light is that it is almost entirely one (actually two very close together) wavelength of yellow light, and that it gives the most illumination for the amount of electricity.  A big problem with this light, though, is that it throws off color perception.  Under sodium vapor light, something blue looks gray.  This makes it hard to, say, recognize your car in a parking lot.
Richard Barrans Jr., Ph.D.