The phrase to give someone the cold shoulder means to be unfriendly; treat them with disdain; or have an unwelcome attitude towards someone.
The origin may be quite simple - if you turn away from someone that dismissive movement could easily have been called the cold shoulder. The phrase seems to date from the nineteenth century.
On the other hand there is a more romantic story. In Victorian times and earlier the guests were given a hot meal while the servants had to make do with the cold shoulder that also servee to provide the host's tea. So if a guest arrived and was provided with the cold shoulder of mutton they were being treated with disdain. There's no evidence to suggest this origin but it's much more fun.
Toby at Six Months
13 hours ago