There is a great story on NPR's website about a man who actually did the "offering your coat" thing, as in the New Testament:
He was walking toward the stairs when a teenage boy approached and pulled out a knife.
"He wants my money, so I just gave him my wallet and told him, 'Here you go,'" Diaz says.
As the teen began to walk away, Diaz told him, "Hey, wait a minute. You forgot something. If you're going to be robbing people for the rest of the night, you might as well take my coat to keep you warm."