Lightning is the product of static electricity within a cloud. It’s literally static discharge—the same as you scuffling your feet across a carpeted room and then reaching for a doorknob or something metal. Your body is superb at transmitting that charge and you produce that mini lightning bolt you feel as a shock. So what does this have to do with a rain or snow cloud? Heat in the air from below the cloud helps it pile high and get countless billions of water droplets rubbing against each other up and down inside the cloud. Eventually enough static electricity is built up to be released as lightning, However, in snow clouds it’s just too cold! Not enough heat to get ice crystals to rub each other and produce static electricity. That’s why places like Arizona or Florida have spectacular lightning storms—they’re warm or hot climates. Not cold and snowy like Minnesota or New York.

But when you do have 'thunder snow' the lightning effect is truly awesome. I've experienced thunder snow twice in the past 50 years in NW Vermont. It does happen, apparently in very rare meteorological circumstances.

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It is! I’ve seen it once in the Sierra Nevada mountains in California, years ago. Spectacular!