Hoar frost is a layer of frost that collects on the surfaces of objects. Imagine a winter scene in which all of the trees and anything outside has a layer of frost over it. That is hoar frost.
Hoar frost is comparable to dew in the way that it develops. Both dew and hoar frost appear when there is more moisture in the air than the air can carry. The same conditions also create rain and snow. A weather analogy could be stated as dew: hoar frost :: rain: snow. Whereas rain and snow are formed high up in the clouds, dew and hoar frost are formed close to the earth's surface.
A discussion of dew and frost requires a discussion of dew point. The dew point at any given time is the temperature of the air when it is completely saturated by water. When the dew point is high, many people would say it is muggy and likely to rain. They would be correct.
When the air is cooled, it loses its water in its various forms. When the cooled air contains enough water to keep the dew point above freezing, then dew is formed. When the air is sufficiently dry to lower the dew point to below freezing, then hoar frost is formed. The freezing point of water, which may be recalled from school, is 0 degrees Celsius and 32 degrees Fahrenheit.
Hoar frost can take many different forms when viewed at a magnification. Some frost flakes have designs similar to snowflakes when magnified. According to the Alaska Science Forum, hoar frost can develop in a number of intricate patterns from plates, needles, and cups to fern-like and feather-like. The form frost appears in depends on the temperature at which the ice crystals developed.
Surface hoar is the type of hoar frost that appears on snow banks, giving it a sparkly appearance. These are the type of frost crystals which are shaped like cups. They are found early in the morning because the sun warms snow banks, melting the ice crystals. They are formed when snow banks are warmed during the day, then the air cools at night. This is the most common form of hoar frost. Most people have woken up and looked out the window to find snow that has fallen in the night, sparkling away in the sunshine.