A cycling vest is an essential piece of clothing. A cycling vest covers the upper body and thus the part where you most often get chilled. Many people start their ride with a vest on, then once they're warm, they take it off and put it in the back pocket of their jersey. It's also very useful if you're riding down hills. On the descents it usually gets cold because of the speed and not pedalling. That's where a windbreaker really matters to keep you from getting cold.
You can get a wind jacket that is rain and windproof, this usually makes sense if you use it in spring or autumn.