Can it be too cold for thunder & lightning?
There can be thunder during a snow storm, but it is rare. A thunderstorm’s intensity is determined by how much instability exists in the atmosphere. The instability is caused by warm air mingling with cold air. During a snow storm, there is usually no warm air, only cold air and colder air. This means that there is a slight instability, enough to maybe create some lightning and thunder, but not a lot. Knowing that, then you can see how there will be less and less lightning as the temperature drops, since there will be less temperature differential in the atmosphere. There can always be lightning, where ever there is a mixing of air masses, but the lower the temperature, the less lightning there is. The link below gives a lot of good information about this and has pictures too. I hope this helps.
Lightning (and thus thunder) works just based on electrostatic principles with the clouds and the earth. It shouldn’t matter how cold it is or whether there’s snow, because as long as there’re clouds static electricity can build up and then be released as lighting. I have seen lighting in “snow” conditions before. It’s possible that when there’s snow on the ground it somehow insulates or otherwise messes with the principles and reduces the chances of lighting, but I doubt it.