An ice storm is distinct from a thunderstorm, though, and a cold weather thing. Also, often enough not very storm-like.
On the other hand, for thunderstorms you typically need a temperature differential. They can happen even in cold weather (typically when it’s getting much colder or warmer) though the chance of hail and/or hail intensity isn’t as high since winter thunderstorms tend to be much less energetic than those during warmer seasons.
