They usually form in one of four ways:
A normal thunderstorm that runs into an area of cold air, and the precipitation falls as snow.
A heavy snowstorm that has strong vertical mixing, giving favorable conditions for lightning and thunder.
Lake or ocean effect thunderstorm
A cold front with extremely cold air aloft and conditions that cause strong vertical movement.
Where most thunderclaps can be heard for many miles, the snow suppresses the sound. If you hear thunder in a snowstorm, the lightning is at most 2-3 miles away on average.
Snow, like rain in thunderstorms, falls heavily in these events. Often people can see 2-4" snow per hour from a thundersnow. Visibility is reduced in these events, even in light winds.
Thundersnow events peak in March, so we could hear more about this going into the late winter and early spring.