USEFULNESS OF FOG LAMPS

A good fog lamp produces a wide, bar-shaped beam of light with a sharp horizontal cutoff (dark above, bright below) at the top of the beam, and minimal upward light above the cutoff. Almost all factory-installed or dealer-optional fog lamps, and a great many aftermarket units, are essentially useless for any purpose, especially for extremely demanding poor-weather driving. Many of them are too small to produce enough light to make a difference, produce beam patterns too narrow to help, lack a sufficiently-sharp cutoff, and throw too much glare light into the eyes of other drivers, no matter how they're aimed.
Good (and legal) fog lamps produce white or Selective Yellow light, and use tungsten-halogen bulbs. Xenon or HID bulbs are inherently unsuitable for use in fog lamps, and blue or other-colored lights are also the wrong choice.
The fog lamps' job is to show you the edges of the road, the lane markings, and the immediate foreground. When used in combination with the headlamps, good fog lamps weight the overall beam pattern towards the foreground so that even though there may be a relatively high level of upward stray light from the headlamps causing glareback from the fog or falling rain or snow, there will be more foreground light than usual without a corresponding increase in upward stray light, giving back some of the vision you lose to precipitation.
When used without headlamps in conditions of extremely poor visibility due to snow, fog or heavy rain, good fog lamps light the foreground and the road edges only, so you can see your way safely at reduced speeds.
In clear conditions, more foreground light is not a good thing, it's a bad thing. Some foreground light is necessary so you can use your peripheral vision to see where you are relative to the road edges, the lane markings and that pothole 10 feet in front of your left wheels. But foreground light is far less safety-critical than light cast well down the road into the distance, because at any significant speed (much above 30 mph), what's in the foreground is too close for you to do much about. If you increase the foreground light, your pupils react to the bright, wide pool of light by constricting, which in turn substantially reduces your distance vision—especially since there's no increase in down-the-road distance light to go along with the increased foreground light. It's insidious, because high levels of foreground light give the illusion, the subjective impression, of comfort and security and "good lighting".
US-DOT headlamps have historically tended to provide relatively low, arguably inadequate levels of light in the foreground and to the sides. Many US DOT headlamps have what seems to be a "black hole" in front of the car, with essentially the entire beam concentrated in a narrow band or ball of light thrown into the distance. With headlamps like these, a decent argument can be made for the use of fog lamps to fill the "black hole", that is, to add-back the missing foreground and lateral-spread light when driving at moderate speeds on dark and/or twisty roads. Of course, lamps to rectify inadequate foreground light must be thoughtfully and carefully selected, correctly aimed and properly used. Otherwise, they're useless at best and dangerous at worst.
In some places, the law prohibits the use of fog lamps without the low beam headlamps also being on. Whether or not this is the case where you drive, it's vital to realize that fog lamp beams, by definition, have a much shorter reach than headlamp beams. If you drive in conditions foul enough to call for the use of fog lamps without headlamps, it's essential to have good fog lamps that are up to the task and are properly aimed, and it's imperative that you slow down because even with high-performance fog lamps, you can't see as far with fog lamps and in poor weather as you can with headlamps and in clear weather.
If the road is wet or slick with ice, but there's no falling precipitation, fog lamps should be used with discretion. Their extra downward light can help compensate for the tendency of water to "soak up" the light on the road from your headlamps. But, this extra downward light hitting a road surface shiny with water or ice will also create high levels of reflected glare for other drivers. Since we're all "other drivers" to everybody else on the road, it's well to think of roadway safety as a cooperative effort. In most driving situations, fog lamps are neither useful nor necessary, but more people use their fog lamps when the prevailing conditions don't call for their use, than use them when the conditions do call for their use. Nobody thinks your car is cool because it has fog lamps, and glare is dangerous, so do yourself and everyone a favor: choose them carefully, aim them properly, use them thoughtfully, and leave them off except when they're genuinely necessary.