Rime is a white or milky and opaque granular deposit of ice formed by the rapid freezing of supercooled water drops as they impinge upon an cold exposed object. Rime is denser and harder than hoar frost, but lighter, softer, and less transparent than glaze. Rime might have long 'feathers' and 'tails' of rough ice granules or might even be a fairly compact coating if favorable conditions for rime formation persisted over a longer time.
Generally the 'feathers' and 'tails' point into the wind, but under calm conditions the 'needles' might grow into every direction. This is why they can be mistaken as hoar frost. However, unlike hoar frost rime is formed by freezing fog or cloud droplets. The tiny supercooled water droplets remain liquid until they come in contact with any obstacle, when they freeze almost instantaneously. If the fog persists for some longer time large amounts of ice can be deposited.
Whereas rime usually builds up moderately in lowland areas it may accumulate to an ice cover of several feet in mountaineous regions. In fact rime ice makes up a significant source for valley glaciers as it breaks away falling into the valley below. Rime usually accumulates best on exposed obstacles, such as trees, radio masts or rock pinnacles. It might sometimes cause some structural damage, but generally far less severe than black ice or glaze.
All images copyright B. Mühr