English similes are fixed expressions, and "as cool as a cucumber" is one of the most commonly used ones. It describes a person who remains calm, relaxed, and unruffled even in a stressful or tense situation. The comparison works because a cucumber's inner flesh feels cool even when the outside temperature is warm, which became a metaphor for emotional steadiness.
None of the other choices form an accepted idiom. "Winter night" and "ice cream" both relate to physical temperature rather than personality or behaviour, so they do not carry the idiomatic meaning of staying calm. "Rock star" is linked to fame, glamour, or confidence, which is unrelated to the idea of composure under pressure.
Because "a cucumber" is the only option that completes the recognised idiom for calmness, the correct answer is option 1, a cucumber.