That example is all right. Usually people talk about it in the past tense. For example, "I spoke to her on the street, but she gave me the cold shoulder". It means to rebuff someone.

Yes. It is usually used in the past tense, however, if I was speaking to someone and wanted to say what you're trying to say there I would word it like this: "He didn't invite me to his party! I'm just going to have to give him the cold shoulder then." haha.

It means to ignore someone totally as if you don't see him/her. This is because he/she has upset you before.