why don't snowstorms produce thunders and lightnings?

why don't snowstorms produce thunders and lightnings?

During summer, the lower atmosphere is full of warm, humid air. Above that, it's cold and full of ice crystals. As the warm air rises, it carries water vapor with it, these molecules brush against the ice crystals, and this friction creates an electric field in the cloud ( like scuffing your feet across a carpet). The ice crystals gain a slight positive charge, and the updraft carries them to the top of the cloud, giving the cloud's bottom a net of  negative charge. Once the difference between the negative charged cloud bottom and the positive charged cloud top becomes great enough, it produce a electrification (discharged as lightning) or a sudden heating and expansion of the air (thunder).

But in snowy months, the atmosphere is cold and dry throughout, so there's no updraft to create friction within the clouds. Lightning and thunders will still occur at the frontal zones, however, where cold air meets warmer air