What is the name for a snowstorm that produces lightning and thunder?

A snowstorm that produces lightning and thunder is called thundersnow. It is a thunderstorm in which snow, rather than rain, is the primary precipitation.

Thundersnow forms when strong upward motion creates enough instability inside a cold-weather storm for electrical charge to separate in the cloud. The same basic process powers ordinary thunderstorms, but cold air is generally less likely to rise vigorously, making thundersnow uncommon. It can occur in powerful extratropical cyclones, lake-effect snow bands, and mountainous regions.

Heavy snowfall often muffles the sound of thunder, making it seem like a distant rumble. Lightning is also less frequent than in summer thunderstorms and is commonly observed between clouds. Thundersnow may bring exceptionally intense snowfall, sometimes around 2 to 4 inches per hour, and it can occur within a blizzard. A whiteout describes severely reduced visibility, while an ice storm involves freezing rain rather than snow.