Thundersnow is probably the most "weenie-riffic" winter weather element. It truly is an exciting concept and combines all the mysterious elements that seem to excite weather enthusiasts. I think it's partially because most weather enthusiasts are snow obsessed, but also because it's an infrequent event, but not so much that it could be deemed as "rare." It was perhaps made most famous by The Weather Channel's Jim Cantore, who seems to always be on the receiving end of thundersnow when he covers winter storms.
It can also occur with a cold frontal passage as well, but more often than not, the differences in air mass from before the front to behind it would have to be fairly extreme or very cold (most often in a secondary push of Arctic or Polar air, as opposed to a generic cold front). Those are most often the 10-20 minute bursts of tremendously heavy snow and whiteout conditions that can occasionally cause massive traffic disruptions.
Now, within the larger scale storms, thundersnow most often forms in the comma head of the cyclone. This is usually on the northwestern side of the storm, which helps the Delaware Valley occasionally see it during offshore tracking nor'easters. You can also occasionally see thundersnow ahead of (north and west of) an approaching cyclone. It normally would occur with an inverted trough that may occasionally form extending out to the north of the main low into the colder air. This is called a trough of warm air aloft (or TROWAL).
In lake effect precipitation, where thundersnow is actually somewhat common, you need to have a certain temperature differential between the lake water and the air at about 5,000 feet. In the upcoming LES entry, we'll discuss this some more.
What thundersnow does usually promise you is heavy snow. Rates usually get to at least 2-3" per hour in thundersnow, and I've seen lake effect bands produce thunder and as much as 5-7" per hour. Think of some of the more absurd rain scenarios you can have with thunderstorms and translate them to winter and you can see just how heavy it can get. Say what you will about winter, snow, cold, etc., but thundersnow to this meteorologist still remains one of the neatest weather elements that exists.
Read more about how thundersnow forms here.
And learn more about where it occurs and some past examples here.