You know it never rains in Southern California . Just because the average rainfall for January says 3", doesn't mean it will rain. It's pretty much a crapshoot out here if it will rain or not. It rained yesterday and this morning, but nothing really major. Depending on what the weather is forcasted for, I would pack warm clothing and an umbrella or plastic poncho if rain is forcasted.
It rarely rains enough in southern CA to warrant boots. If you are coming in Jan., you may want to pack them just in case (since Jan/Feb would be the time it does rain that much, if ever), but you probably will not need them. Even in the rain, it rarely goes below the 50s, so a long-sleeved shirt, sweater, rain-resistant windbreaker (or poncho/slicker) and an umbrella should be good preparation for rainy days. You might want to carry a backpack with a spare change of clothes inside of a plastic bag, though.
Chances are, this won't be necessary, but better to be prepared. I think this winter is going to be a cold one.