Types and Fall
There are different types of snow crystals and snowfalls. The types of snow crystals are covered below as well as some of the most interesting and important snowfalls that would be important to know.
The four types of snow crystals are:

hoarfrost       snowflake1 
 Hoarfrost (worldgenius.com)        Snowflake (quantamagazine.org)
                               
Snowflakes - Precipitation in the form of single or clusters of ice crystals that resemble flakes. These are often symmetrical, but each are unique in that no two snowflakes are the same.

Hoarfrost - Ice crystals falling may land on colder surfaces or at below freezing than atmospheric temperatures, allowing these ice crystals to rapidly freeze. This freezing is hoarfrost and it may cover plants (beautiful).

Graupel - Graupel are snow pellets (ice crystals) that from when fog freezes and condense on snowflake; if its size becomes larger than 5 mm, it's called hail.

Polycrystals - Snowflakes composed of numerous ice crystals are polycrystals.

Snowfalls

winterstorm
Winter storm in November 2020
Photo by Alexis Francisco

Blizzard - A powerful winter/snow storm characterized by strong winds and subfreezing temperature, reducing outside visibility and lasts at least three hours.

Snow squall - A short, but intense snowfall accompanied by strong winds and reduces visibility.

Winter storm - At least two combinations of severe and dangerous winter conditions such as heavy snowfall with strong winds, blowing snow, and extreme cold.

Snow flurry - The light snow that usually melts immediately or a few seconds after falling on pavements or surfaces. They usually fall for a short period of time and different intensities.

Thundersnow - A poorly understood rare event that occurs in the winter. It is a convective storm that occurs when snowstorms and snowfall produce lightning and thunder. To create a convective storm, consequently a possible thundersnow, are: moisture, lift, unstable temperature, and cold air.