Here in norther Canada, I have never seen lightening in winter – when the surface temperatures are below freezing. But the upper atmosphere where the stores clouded reach to are always far below freezing.
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**Second part first:**
For a spark to jump across a gap (like lightning) there needs to be a high enough potential difference that air ionises.
The potential difference required depends on what the gas is made of – so for example if the atmosphere was made of argon, there would essentially be no lightning, ever.
In the winter, air is dryer, so there are fewer water molecules in the air. The water molecules did a lot of the heavy lifting to conduct the charge, so without them the potential difference needed is higher. Lightning isn’t impossible, but it will be rarer the drier the air is.
**First part (I understand this part less):**
Clouds involve a lot of water molecules stirring around. Warmer air is less dense so it rises. The electrons are also typically in higher energy levels, so they’re a bit more likely to leave the atoms when compared to colder air. As the warm air moves upwards, it loses electrons to the cold air, making the cold air negative and the warm air positive. This is the same as your socks transferring charge with a carpet due to friction. Since earth is roughly neutral, that means there is a big pd between the cloud and the ground.
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