Yellow light supposedly penetrates further because of its long wavelength, but it's still much smaller than fog particles. The scattering effects of fog are essentially independent of wavelength. Any color would do just as well. So does white, and there's no reason to put on a filter.
But yellow lights are traditional, so that's what you get. It's actually a particular shade of yellow, since road regulators don't want a rainbow of shades on the road, but legally it can be white as well. (In fact, the fog lights on my Honda Fit are white.) Red and blue are reserved for emergency vehicles, so yellow is what you get.
I think that there's also a marketing effect here: yellow says, "Hey, I have fog lights." Many "fog lights" are just for show and don't do much good. Fog lights mounted high up just glare right back into your eyes. Fog lights have to be mounted low, since the whole point is to make sure you can see the crucial thing, the edge of the road and lane markings.