Actually, I keep two good hangers in my office. One for my jacket, and the second for my coat, when worn. If you are hanging up your jacket, at least make sure it's on the same quality of hanger you have at home, a wire hanger from the cleaners doesn't quite work.
As I typically have lunch at my desk, I don't wear my jacket to a restaurant. But, should I venture out for a meal, the jacket stays on. What I do find odd is that when the weather is cold, I see men keeping their coats at the table, either on an extra chair or the back of their own. There is a reason for a coat check, and not using it makes you appear either cheap, or suffering from separation anxiety.