Can 'thundersnow' be severe? The definition used for a thunderstorm and some other things become important.
Conventionally, a thunderstorm is considered to be a cumuliform cloud which has lightning and thunder. However, many of us have experienced and are aware of some intense 'thunderstorms' that have virtually no lightning (most commonly, minisupercells). These storms can most certainly be severe and even produce tornadoes. In
Severe Convective Storms, Doswell uses the term "deep moist convection (DMC)" rather than "thunderstorm." This allows for the inclusion of nonthundering convection . I like this way of thinking.
Thundersnow is convective in nature. The heaviest snowfall rates come from convective snowstorms. So the thunder and convection criteria are met in the first case and the convection criterion is met in the latter. As for these meeting the severe criteria, it would be pretty rare, but certainly possible. Severe storms require moisture, instability, lift, and shear; plentiful moisture is very rare in cold air masses though lift and shear (dynamics) certainly aren't. Hail and tornadoes would be much less likely than severe convective winds.
This is what occurred in the Midwest on 11 February 2003. A strong dynamic system moved through the region, spawning thundersnowstorms. These storms exhibited
frequent lightning and severe winds. ILX issued some severe thunderstorm warnings for it and took some heat for doing so. They can't really be faulted though as convection, lightning, and severe winds were all present. There was severe magnitude gradient winds associated with this system however, as well. As an aside, snow rollers were also produced over a wide area with this system.
http://www.crh.noaa.gov/ilx/events/roller.htm
Scott