Green’s Dictionary of Slang

1. a frosty reception.

1899–1900

C.L. Cullen Tales of the Ex-Tanks 145: The frontless man is the recipient of the dead face, otherwise the cold storage countenance.

2. (Aus.) cheek, impudence.

1912

Bulletin (Sydney) 12 Dec. 29/3: But I hadn’t got the end of that guy – no, sir. He had cold storage enough to come to me three years after and want me to go into something else.