Formal Definition: Snow is precipitation in the form of ice crystals, mainly of intricately branched, hexagonal form and often agglomerated into snowflakes, formed directly from the freezing [deposition] of the water vapor in the air.
Snow begins aloft when temperatures drop below freezing. As the temperature drops, the water vapor that makes up the clouds freezes, forming ice crystals. Many of these ice crystals join together to form a snowflake and begin to fall to the ground. In order for the snowflake to remain as such until it hits the ground, it must pass through a cold (below freezing temperatures) layer all the way.
Can snow occur with surface temperatures above freezing? YES!. Sometimes a very shallow warm layer (above freezing temperatures) will form at the surface. Since the depth of this layer is very shallow, there is not enough time for the snowflake to melt before hitting the ground, allowing for the snowflake to remain intact.
Snow grains are formed by a similar process but are usually less than 1 millimeter in diameter.
Formal Definition: Pellets of ice composed of frozen or mostly frozen raindrops or refrozen partially melted snowflakes. These pellets of ice usually bounce after hitting the ground or other hard surfaces. Heavy sleet is a relatively rare event defined as an accumulation of ice pellets covering the ground to a depth of 1/2 inch or more.
Sleet begins as snow aloft in the cloud layer. As the snow falls, it partially melts as it passes through a shallow warm layer. Upon entering a second layer of below freezing temperatures at the surface, it freezes once again to form the ice pellet.
Formal Definition: Precipitation that falls as a liquid but freezes into glaze upon contact with the ground. When the liquid particle has a diameter of less than 0.5 millimeters, the term freezing drizzle is used.
Freezing rain begins with either a rain drop or a cold layer aloft creating snow. As this droplet falls to the ground, it encounters a deep above freezing layer that allows for the droplet to either remain a rain droplet or for the snowflake to melt completely, creating rain. A shallow layer of sub freezing temperatures at the surface causes the rain droplet to freeze upon impact with the ground.
ConclusionSnow forms with a below freezing temperature layer (less than 32F) from cloud to the ground.