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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Thundersnow is a thing but it’s rare. Very cold air doesn’t contain much water vapour, and the “power source” for thunderstorms is water vapour. Without much water vapour it’s hard to get enough energy to get a storm going.
You’re right that it’s generally freezing up at the altitudes where the *tops* of thunderstorm clouds go, but that’s not where those clouds started. Thunderclouds start with warm moist air at low altitude. The warm air starts to rise, and as it rises it cools. Eventually it saturates (100% relative humidity) and the water vapour starts to condense, which releases TONS of heat. That boosts the temperature above what it otherwise would be, the warm air stays warm longer, and it keeps rising more, cooling more, condensing more, and so on.
The voltage comes from water droplets rubbing against each other. Think fuzzy socks on your wool carpet, only bigger. Much much bigger.
**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.
Winter lightning does exist “thundersnow” – in [Edinburgh we had a burst 2 years ago](https://www.bbc.co.uk/news/uk-scotland-edinburgh-east-fife-55184493), it was unbelievably loud as the snow holds the sound in place, and unbelievably bright as the snow lit up with the lightning. I honestly thought I was having some form of stroke.
Thunderstorms don’t build up a voltage but instead a charge. Charge is built up from a variety of ways but simply, a transfer of electrons from one *insulator* to another.
You’ve probably at one point rubbed a balloon on your head and had your hair get attracted. This is due to the potential difference created between the balloon and hair (similar to how a magnet works, + and – attracts)
When water vapor transfers electrons in the cloud, parts of it become changed differently. This creates a potential difference between the ground and clouds.
When there is enough potential difference, the air below become ionized. (this is the start of the lightning) The bolt travels down turning atoms in the way into ions. When it finds a way to ground, a concentrated current flows through the path of ions created and applies a voltage across the air, partially balancing the potential difference, until there isn’t enough energy for the ions to remain ions and the air returns to normal.
The winter air have different conditions and may be dryer. This dryness or lower water concentration can mean less potential difference or more resistance in the air (its harder to create ions in the air). It could also simply be that less clouds are created or that the movements in the clouds are slower from less temperature differences. Any factor to reduce charge buildup or increase resistance in the air can cause less lightnings. (it could also be that the clouds are higher in the air).
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