Would you offer someone you don't know your coat at a party if they said they were cold?

My god brothers mother-in-law was opposite to us at the table, sitting under the overhead heater in the beer garden.
And his wife next to me, anyways she said she was a little cold as she had her shoulders exposed.
She had left her jacket in the car.
I had mine in my lap but didn't offer mine.
So her daughter (god brother wife) asked him if he was cold...
He then gave his jacket to his mother in law.

It's not that I couldn't offer, I just didn't because well I don't know her.
Also why be sat somewhere for 2 hours cold when you could return to the car to get your coat!?