When snow forms, water vapor converts directly into ice without becoming liquid first - this process is known as sublimation. Sometimes raindrops do freeze as they fall, but this is called sleet and not snow.

Snowflakes and snow crystals are made of crystallized ice; A snowflake is a conglomeration of several snow crystals. Most snow crystals are simple hexagonal prisms and easily bind to other snow crystals, if the weather conditions are right.

Normally, snowflakes are less than half an inch across. When the weather is at a near-freezing temperature, the air is unstable (convective currents or other drafts or motion of air, such as turbulence), and if there is light wind, there is a chance that the snowflakes can become up to two inches across. Studies show that snow crystals tend to form simpler shapes at lower humidities and more complex shapes at higher humidities. The most extreme shapes and largest flakes form when the humidity is relatively high.

The hexagonal symmetry of snowflakes is because of the symmetry of the ice crystal lattice. Water molecules hook up to form ice in a hexagonal lattice, and the molecular symmetry is imparted to the snow crystal form via faceting. In particular, tiny snow crystals are usually in the form of small hexagonal prisms, which is how the six-fold symmetry of snowflakes gets its start.

Close inspection of a snowflake reveals that the individual crystals are pretty clear. However, as light shines through a snowflake, part of the light gets reflected - kind of like the sheen you see on a puddle. Generally speaking, snow and ice are white in color. This is because most of the light that strikes the snow is reflected back to us with no pigmentation - light is naturally white, full pigmentation is black. This isn't the case with the light that travels through the snow, however - since the light is travelling through thousands of flakes, bouncing around, reflecting here and there, and travelling maybe a meter - maybe a mile - through a bank of snow, the light changes color. This is because red light is more readily absorbed by the snow than blue light - and this is why snow looks blue inside ice caves or even if you just poke your finger into the snow. This effect is referred to as spectral selection. For spectral selection to show a visible difference, the light must travel a minimum of one meter through an "average" bank of snow.

Sources: nsidc.org/snow, meteorology class, caltech.edu.