You may be asking yourself why don't the droplets freeze if the air temperature is below freezing? The reasons are pretty technical, having to do with nucleation and latent heating, so we won't go into it here. But suffice to say, if the air temperature is between 0°C and -15°C (between 32°F and 5°F), the cloud (or fog) will be made up entirely of liquid droplets. We call these super-cooled liquid water. If the temperature is colder than that, ice crystals start to form.
A website from CalTech has an excellent overview of frost vs rime, along with great pictures the two. Visit it at: http://www.its.caltech.edu/~atomic/snowcrystals/frost/frost.htm
For the Inland Northwest, we often experience extended periods of dense fog in the winters which lead to heavy accumulations of rime on trees and other objects. One event in January 2009 created some beautiful rime on the trees at our office west of Spokane.
This next image shows how the rime crystals actually formed in a preferential direction, due to the wind. While you might guess that the light wind was blowing left to right, you'd be wrong. The wind was blowing lightly (1-3 mph) from the right to left, and the crystals grew into the wind.
While this rime does make for some neat pictures, it also can cause problems. During this 2009 event, the rime accumulated power lines along Highway 2 west of Spokane. This rime accumulation actually led to power outages for many customers in this area. Here's a picture taken by the Avista repair crews. The weight of the rime caused the power lines to lower almost to the ground.
And here's the rime accumulation on a power substation.
Lastly, anyone who skis our area mountains probably has seen some even more impressive rime on the trees. Here's a couple of examples from Mount Spokane.