1.To snub someone; to assume a distant manner, or show indifference. The term dates from the early nineteenth century and was frequently used by Sir Walter Scott. It is believed to come from the custom of serving hot meat to welcome guests, and of serving a cold shoulder of mutton or beef, considered a much inferior dish, when they had outstayed their welcome.
2.To intentionally appear disinterested toward one; to snub. This phrase usually refers to the act of ignoring someone. It originated with the 19th-century practice of serving of a cold shoulder of meat to tiresome guests.