Aside from the snow, we've had a few reports of lightning with our November Snowstorm. But I sure got a lot of puzzled looks when I mentioned it was "thundersnow."
The lightning during snow isn't any more special than regular lightning as far as how it's formed, but if you've heard it, you might notice it can seem much louder than regular lightning.
The reason is thunder is louder in a snowstorm because cold, dense air is a much better conduit of sound.
(I should clarify -- it doesn't mean the thunder is louder than normal, just that the sound travels more efficiently, so it's louder when you hear it than you'd expect.)
Bolts can also reportedly quite bright -- many say brighter than a usual lightning bolt. That's likely due to the snowflakes doing a good job of reflecting the light around.
Now, many people associate thunderstorms with warm events, but you can get thunderstorms during cold and snow storms. All you need is for it to be even colder in the upper atmosphere and some sort of mechanism to force the air upward. It's rare, since it's usually when it's this cold around here, we don't get much colder, but in this case, even colder air from the arctic was moving in Monday evening, and converging winds in the lower levels forced air upward, causing cloud development and, eventually, thundersnow.
Lightning, in a very oversimplified way, is caused by a build up of static charge by the air particles moving around inside the cloud, much like scuffing your socked-feet on the carpet. The charge then discharges in what you see as lightning.