Snow and Convection

Radar image from the National Weather Service in Duluth, MN
Introduction
Thundersnow is THE ultimate winter experience. This author is fortunate to have experienced storms with thundersnow more than just a few times, mostly in Duluth, MN, including two storms that produced cloud-to-ground lightning. I also observed thundersnow in Columbia, MO, Kansas City, MO, and Topeka, KS. The number of thundersnow enhanced storms in Duluth based on personal observations is fourteen from Winter 2001-2002 to Winter 2022-2023. The "Favorite Storms" page of this website documents several of the storms. Again, the observations were personal. Thunder was likely not observed in all the same storms at the National Weather Service. Note that lightning discharges do not have to attend convectively enhanced snow.
Where does thundersnow occur?
To get thundersnow you obviously have to get snow. Locations that don't get much snow are a lot less likely to get thundersnow. Climatological studies done for the "Research on Convective Snows" project at the University of Missouri-Columbia indicate that thundersnow is most common in certain areas of the United States. Those areas are the central United States, locations downwind of the long axis of the Great Lakes that experience strong single-banded lake effect snow squalls, and parts of the Intermountain Region of the West. Utah showed one of the highest concentrations. An example of a place that rarely gets thundersnow is Portland, Oregon. Rare, of course, does not mean never. On January 10 to 11, 2017, heavy snow, accompanied by thunder, accumulated at rates up to 2 inches per hour.
The central United States
More specifically for the central United States, the same study showed that a higher concentration of thunder reports extended from the central High Plains and the Texas Panhandle, east and northeast through the Middle and Upper Mississippi Valley. The observations typically occurred from northeast to northwest of the center of a strong surface low pressure system where instability was elevated above the surface. Thundersnow can still occur with surfaced based convection along cold fronts and with scattered showers enhanced by diurnal heating. Thundersnow can also occur in storms with a weak surface low pressure system if atmospheric processes still produce a condition where instability and vertical motion overlap. The occurrence of thundersnow in mountain ranges is aided by orographic lift helping to initiate thunderstorm development and the fact that the high elevations poke up into air cold enough for snow to reach the ground.
Assessing stability in cold saturated air
One way to determine the potential for convection in cold saturated air is to examine equivalent potential temperature, also called theta-e. Theta-e is a meteorological quantity that conveniently incorporates temperature and moisture into one variable. Both temperature and moisture influence stability in the atmosphere. Theta-e typically increases with height which is stable. Meteorologists can examine numerical forecast model data to look for layers where theta-e decreases with height or is at least near neutral. The National Weather Service glossary contains a precise definition of theta-e.References
National Weather Service GlossaryJeff Haby's discussion from theweatherprediction.com
The "Research on Convective Snows" project at the University of Missouri-Columbia
Morales,R. F., 2008: The Historic Christmas 2004 South Texas Snow Event: Diagnosis of the Heavy Snow Band. Bull. Amer. Meteor. Soc., 2, 135-152.
Market, P. S., C. E. Halcomb, and R. L. Ebert, 2002: A Climatology of Thundersnow Events over the Contiguous United States. Wea. Forecasting, 17, 1290-1295.
Market, P. S., A. M. Oravetz, D. Gaede, E. Bookbinder, B. Pettegrew, and R. Thomas, 2004: Proximity sounding composites of Midwestern thundersnow events. 20th Conference on Weather Analysis and Forecasting, Seattle, WA, Amer. Meteor. Soc., p4.2.