The image is anchored in classical Chinese:
汉·
王逸《
正部论》compares strict governance to ice and frost ("
政如冰霜"), and
元·
王实甫《
西厢记》 describes Madam Cui's discipline as
凛若冰霜 — the same metaphor in a near-identical phrase. Modern
冷若冰霜 narrowed to describe interpersonal coldness, often a beautiful but distant woman.