Thundersnow occurs when a thunder and lightning storm takes place while it is snowing and most often occurs towards the end of winter or the beginning of spring. Thundersnow is similar to a normal thunderstorm with the important difference that snow falls instead of rain.
A thunderstorm takes place when moisture evaporates rapidly from the ground up to the sky creating instability in the atmosphere. This normally happens in the summer because there is more heat from the sun to instigate the evaporation of groundwater.
Typically, if the weather is warm enough for this first stage to occur then it will not be cold enough to produce snow. In fact, it is seemingly paradoxical that the climate could be warm enough to evaporate lots of water from the ground and at the same time cold enough to turn raindrops into snowflakes. However, thundersnow relies on these exact two things happening.
In order to produce the rare phenomenon of thundersnow, the layer of air above the ground needs to be significantly warmer than the layers of air above. In this case, water will evaporate into the atmosphere creating the instability needed to produce a thunderstorm while precipitation from that thunderstorm will be turned into snow in the cold sky as it falls. Conditions such as these are usually only found as winter moves into spring.