A low one, gives a soft shadow. White is no more realistic for fog than black is for shadows. Try for pastels if you want a nice day time fog. Go for grays if you want the maritime fog. Yellows, oranges or browns for sunsets, sunrises or approaching storms.
Fog is much heavier and thicker than haze and tends to block out the light.
Haze is made up of much smaller, less densly packed particals and bends the light instead of blocking it. Use greens, oranges, or browns to create smog. Use oranges, lighter browns, or grays for forest fires. Use bright red or magentas for approaching sea storms. This sets the color of the top of the sky.