"Man, you wanna get past the cops when they start askin' about tonight? Ya play it cool. Ya wanna live in this lousy world? Play it cool."
(~Ice to the Jets after Riff's death)
Riff was killed by Bernardo during the rumble with the Sharks, at which point Ice took command of the Jets. He is also the best fighter in the Jets, as evidenced when, during their war council with the Sharks, Riff selects Ice to go one-on-one against Bernardo.
Like some of the other Jets, Ice's nickname is indicative of his personality; he is stern and no-nonsense, but also level-headed and slow to anger. On the rare occasion Ice does lose his temper it is only to re-exert his command and keep the other Jets in line.
After Riff is killed, most of the other Jets, especially Action, are hell-bent on vengeance against the Sharks, but Ice warns them all to not let their emotions get the better of them- in other words, "play it cool".
Ice is the one who makes Anybody's an official member of the Jets after she informs them of Chino's intention to shoot and kill Tony after he killed Bernardo in the rumble.
Ice is not present when the other Jets attack and nearly rape Anita, so it is unknown whether or not he would have taken part, but given his level-headedness, he presumably wouldn't have condoned the other Jets' actions, and might've heard her out.
After Tony dies, the Jets and the Sharks are about to fight, but Maria stops them, and almost kills Ice with Chino's gun, the gun he used to kill Tony.
The character of Ice was created specially for the 1961 film. His character replaced that of Diesel from the original play.