I'm not sure if anyone included a watch cap on their list but it is a great item year round.
I understand that LA isn't exactly the coldest state in the union, but if you are cold and possibly wet a nice, warm wool or fleece watch cap can make a world of difference.
They are usually cheap, not too expensive, and very compact.
I would stay away from the acrylic ones they don't have very good heat retention when wet.