Fog is defined as "condensed water vapor in cloudlike masses lying close to the ground and limiting visibility". Ice fog is, logically enough, fog formed from the suspension of particles of ice, rather than droplets of water. Normal fog is formed when warm, moist air comes in contact with cooler air. The warm air cools rapidly, and the water vapor condenses into droplets of water which are small enough to remain suspended in the air, forming fog. Ice fog, also called pogonip, is formed under conditions of extreme cold (around -30 F). Water vapor from, for example, car exhaust hits this cold, dry air and goes from 250 F to -30 F in a few seconds. The water vapor in the exhaust is flash frozen into particles of ice so small that they can remain suspended in the air, creating ice fog.
Ice fog has been targeted as a factor in poor winter air quality in cities with cold climates. Aside from frozen water, ice fog contains carbon dioxide, carbon monoxide, and other chemicals expelled into the air from car exhaust, power plants, factories, etc. These chemicals are captured in ice particles and hang in the air, forming a smoggy, brownish haze.
Fog disperses when the air warms up enough that the rate of evaporation exceeds the rate of condensation of water vapor. In the same way, ice fog clears up when the air temperature warms up to the point where ice particles are sublimated into water vapor faster than they are formed. Ice fog may also be dispersed by wind, or may thin out by precipitation. Just as water droplets gradually precipitate out of fog (onto the ground, car windows, pedestrians), so ice particles precipitate. The process is generally slow, as the ice particles in question are tiny - 10 of them side by side are about as thick as a sheet of typing paper - but a film of powdery frost will eventually be deposited on everything not smart enough to be indoors.
Information was taken from the Alaska Science Forum (http://www.gi.alaska.edu/ScienceForum), and the Bad Meteorology web site (www.ems.psu.edu/~fraser/BadMeteorology.html)