"As cool as a cucumber" is a well established English idiom meaning very calm, composed, and not anxious, even under pressure. It refers to a person's temperament rather than actual temperature, since a cucumber's flesh stays cool to the touch even in warm weather.
"The winter night" describes literal cold temperature, not the idiomatic sense of emotional calmness, so it does not complete the fixed expression. "An ice cream" is also about physical coldness, not composure, and is not part of any standard idiom. "A rock star" relates to fame or style, not calmness, and forms no recognised simile with "cool".
Since English has one fixed idiomatic phrase for describing a calm person, "as cool as a cucumber", option 1 is correct.