He describes the answer the best...
On the day the first headlight was put in a car - they didn't have halogen lamps that were powerful enough to brighten a portion of the road ahead. So they did what they could with electric bulbs (coils n all).
But nowadays LEDs are catching on and it's trickling down from the very large and luxurious automobile makers to the affordable ones.
It's what happens when you subtract blue from the output of a lamp producing white light. But first, what means "white light"? Under US Federal Motor Vehicle Safety Standard number 108 and Canadian Motor Vehicle Standards 108 and 108.1, headlamps as originally installed on motor vehicles (and as installed by anyone other than the vehicle owner) must produce white light.
The relevant SAE (and identical ECE) color standards define "white" light as a rather large range within the CIE 1931 color space. That's why both brownish sealed beams and bluish HID headlamps are considered "white". It's also why "blue ion" or "crystal blue" bulbs with blue-pass dichroic filters sold to poseurs who want to try to pretend they have HIDs are not considered "white". The light can tend towards a yellow tint to a certain degree and still qualify as acceptable "white" light.
In 1936, the French for tactical reasons wanted a way to identify the registration nationality of vehicles at night. However, they did not want to reduce roadway safety, and wanted in fact to improve it if possible. So, they figured to remove the blue from the output spectrum of their vehicles' front lamps.
White light with the blue component subtracted is known as "selective yellow" light. It is a pure yellow color with little or no orange component—hence the French yellow headlamps. Yellow lamps have consistently over the years been subjectively ranked as better in poor weather and lower in glare than white ones, but is the effect real? Or is it just a subjective impression? One problem with this conclusion as drawn from the French experience with selective-yellow headlamps in France is that when the question was being considered, the lamps that were being compared with white lamps reduced the absolute intensity of the beam by about 12 percent. This fact may have had a part in reducing the glare. Because the requirement for yellow light no longer exists (though it remains allowed in many countries) we probably will never know the vagaries of the answer to this question.
What explains the persistent subjective preference amongst experienced poor-weather drivers for yellow fog lamps, despite decades of white fog lamp prevalence?
Selective yellow light can improve a driver's ability to see in fog or rain or snow, but not because it 'penetrates fog better' or 'reflects less off droplets' as is commonly thought. That effect is known as “Rayleigh scattering”, and is why the sky appears blue. However, it occurs only when the droplet size is equal or smaller than the wavelength of the light, which is certainly not the case with ordinary fog, rain or snow. Roadway Fog droplets are several orders of magnitude larger than visible light wavelengths, so there's no Rayleigh scattering.
So, why do yellow fog lamps seem to work better? It's because of the way the human eye interacts with different colors of light. Blue and violet are very difficult for the human optical system to process correctly.
They are the shortest visible wavelengths and tend to focus in front of our eyes' retinae, rather than upon it.
To demonstrate this to yourself, find a dark blue store front sign or something else that's a dark, pure blue against a dark background in the absence of white light—from any appreciable distance, it's almost impossible for your eyes to see the blue lighted object as a sharply defined form; the edges blur significantly. Deep blue runway lights exhibit the same effect; check it out the next time you land at night. Blue also is a very difficult color of light to look at; it stimulates the reaction we call glare. Within the range of allowable white light, bluer headlamps have been shown to be 46% more glaring than yellower ones for a given intensity of light — see studies here and here. So, it seems pulling the blue out of the spectrum lightens the optical workload and reduces glare.
For a more detailed examination of this effect with respect to driving in foul weather, see Bullough & Rea's study on the topic.