Frost different from rime ice
Frost is a thin layer of ice on a solid surface, which forms from water vapor in an above-freezing atmosphere coming in contact with a solid surface whose temperature is below freezing, and resulting in a phase change from water vapor (a gas) to ice (a solid) as the water vapor reaches the freezing point. In temperate climates, it most commonly appears on surfaces near the ground as fragile white crystals; in cold climates, it occurs in a greater variety of forms. The propagation of crystal formation occurs by the process of nucleation.
The ice crystals of frost form as the result of fractal process development. The depth of frost crystals varies depending on the amount of time they have been accumulating, and the concentration of the water vapor (humidity). Frost crystals may be invisible (black), clear (translucent), or white; if a mass of frost crystals scatters light in all directions, the coating of frost appears white.
Types of frost include crystalline frost (hoar frost or radiation frost) from deposition of water vapor from air of low humidity, white frost in humid conditions, window frost on glass surfaces, advection frost from cold wind over cold surfaces, black frost without visible ice at low temperatures and very low humidity, and rime under supercooled wet conditions.Plants that have evolved in warmer climates suffer damage when the temperature falls low enough to freeze the water in the cells  that make up the plant tissue. The tissue damage resulting from this process is known as "frost damage". Farmers in those regions where frost damage has been known to affect their crops often invest in substantial means to protect their crops from such damage.Formation
If a solid surface is chilled below the dew point of the surrounding humid air, and the surface itself is colder than freezing, ice will form on it. If the water deposits as a liquid that then freezes, it forms a coating that may look glassy, opaque, or crystalline, depending on its type. Depending on context, that process may also be called atmospheric icing. The ice it produces differs in some ways from crystalline frost, which consists of spicules of ice that typically project from the solid surface on which they grow.
The main difference between the ice coatings and frost spicules arises because the crystalline spicules grow directly from desublimation of water vapour from air, and desublimation is not a factor in icing of freezing surfaces. For desublimation to proceed, the surface must be below the frost point of the air, meaning that it is sufficiently cold for ice to form without passing through the liquid phase. The air must be humid, but not sufficiently humid to permit the condensation of liquid water, or icing will result instead of desublimation. The size of the crystals depends largely on the temperature, the amount of water vapor available, and how long they have been growing undisturbed.
As a rule, except in conditions where supercooled droplets are present in the air, frost will form only if the deposition surface is colder than the surrounding air. For instance, frost may be observed around cracks in cold wooden sidewalks when humid air escapes from the warmer ground beneath. Other objects on which frost commonly forms are those with low specific heat or high thermal emissivity, such as blackened metals, hence the accumulation of frost on the heads of rusty nails.
The apparently erratic occurrence of frost in adjacent localities is due partly to differences of elevation, the lower areas becoming colder on calm nights. Where static air settles above an area of ground in the absence of wind, the absorptivity and specific heat of the ground strongly influence the temperature that the trapped air attains.Types
Hoar frost
Hoar frost, also hoarfrost, radiation frost, or pruina, refers to white ice crystals deposited on the ground or loosely attached to exposed objects, such as wires or leaves. They form on cold, clear nights when conditions are such that heat radiates into outer space faster than it can be replaced from nearby warm objects or brought in by the wind. Under suitable circumstances, objects cool to below the frost point of the surrounding air, well below the freezing point of water. Such freezing may be promoted by effects such as flood frost or frost pocket. These occur when ground-level radiation cools air until it flows downhill and accumulates in pockets of very cold air in valleys and hollows. Hoar frost may freeze in such low-lying cold air even when the air temperature a few feet above ground is well above freezing.
The word "hoar" comes from an Old English adjective that means "showing signs of old age". In this context, it refers to the frost that makes trees and bushes look like white hair. 
Hoar frost may have different names depending on where it forms:White frost
White frost is a solid deposition of ice that forms directly from water vapour contained in air.
White frost forms when relative humidity is above 90% and the temperature below −8 °C (18 °F), and it grows against the wind direction, since air arriving from windward has a higher humidity than leeward air, but the wind must not be strong, else it damages the delicate icy structures as they begin to form. White frost resembles a heavy coating of hoar frost with big, interlocking crystals, usually needle-shaped.Rime
Rime is a type of ice deposition that occurs quickly, often under heavily humid and windy conditions. Technically speaking, it is not a type of frost, since usually supercooled water drops are involved, in contrast to the formation of hoar frost, in which water vapour desublimates slowly and directly. Ships travelling through Arctic seas may accumulate large quantities of rime on the rigging. Unlike hoar frost, which has a feathery appearance, rime generally has an icy, solid appearance.