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1816, in the figurative sense of "icy reception," first in Sir Walter Scott, probably originally a literal figure, but commonly used with a punning reference to "cold shoulder of mutton," considered a poor man's dish and thus, perhaps, something one would set out for an unwanted guest with deliberate intention to convey displeasure.
How often have we admired the poor knight, who, to avoid the snares of bribery and dependence, was found making a second dinner from a cold shoulder of mutton, above the most affluent courtier, who had sold himself to others for a splendid pension! ["No Fiction," 1820]
To “give someone the cold shoulder” is to ignore someone deliberately: “At the party, Carl tried to talk to Suzanne, but she gave him the cold shoulder.”
A deliberate snub; display of chilly contempt (1816+)verb
: I cold-shouldered him and he looked puzzled (1845+)