Is flying in the snow an idiom?

No.

The four-character word "Flying in the Snow" is an idiom derived from allusions. "Flying in the Snow" has no allusion origin, so it is not an idiom.

Chinese idioms (Pinyin: hànyǔchénɡyǔ) are fixed phrases in the Chinese language that have been formed through long-term use and tempering. Derived from ancient classics, famous historical stories or people's spoken words, the meaning is incisive and often hidden in the literal meaning. It is not a simple sum of the meanings of its constituent components, but has a holistic meaning.