What fun!
Pretty dramatic to see I imagine!
I have seen it here even in the Pac Northwest - but not with really exciting or dynamic thunder and lightning.
To have thunder and lightning occur requires two air masses colliding or one passing over the other with sufficiently different densities. The lower density air has to be below the higher density air, creating the instability that makes the needed updraft and turbulence. This pretty much means the air masses must have very different temperatures, though differences in humidity can increase the density difference too. These are the same conditions as create tornadoes actually.
There is nothing about this condition that says the neither air mass can be cold enough for snow. But usually if it is that cold, it is not as likely that there will be another air mass warm enough in the area to generate the instability needed.
In the plains states of the midwest and down into the South, these conditions can happen pretty often I would think, with those huge cold Norther air masses coming down and colliding with the more tropical air from the South. That happens on the East coast too, but probably not as often.
Here in the Northwest (except in the mountains) we rarely get enough difference between the air masses for thunder and lightning, and only very rarely does it get really dramatic. Usually we get it if the inland air gets warmed enough by the sun and a cold enough, wet air mass comes in off the ocean, usually from the Northwest out of the Aleutians of Alaska.