The lightning during snow isn't any more special than regular lightning as far as how it's formed, but many across the Puget Sound region awakened this morning wondered why it seemed much louder than regular lightning.
The reason is two-fold. For one, the bolt struck near Seattle, so a lot of people heard it. Second though, 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.)
The bolt was 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, arctic air was moving in aloft over the milder air that moved in Wednesday, and the converging winds in the lower levels forced the air upward.
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.