How do you say jack frost in Japanese?

There isn't a direct, single translation for "Jack Frost" in Japanese that captures the same cultural connotation. The closest you could get would depend on the aspect you want to emphasize:

* If emphasizing the mischievous sprite aspect: You could use a descriptive phrase like 霜の妖精 (shimo no yōsei), meaning "frost fairy," or いたずら霜 (itazura shimo), meaning "mischievous frost."

* If emphasizing the cold weather aspect: Simply saying 霜 (shimo) - frost - or 寒波 (kanpa) - cold wave - would suffice, depending on the context.

Therefore, there's no single "correct" translation. The best option depends on the specific context in which you're using the phrase.