I ride my bike to commute to work no matter the weather. I have found that the key to dressing for winter riding is having a cool torso as you start off on your ride. Your upper body will warm up quickly and it is all too easy to start sweating even in the coldest temperatures. 

For my base layer I usually wear a merino wool or wool/polyester mix long sleeve shirt, a thin merino wool sweater and then some sort of wind proof jacket. You can pick up merino wool sweaters a good price if you are a consistent shopper at second hand clothing stores. A jacket with sleeve vents is useful if the weather gets unexpectedly warmer. You can also unzip your jacket if you need to cool off. In cool weather, I wear shorts over bike tights. Bike tights often don't have pockets, so shorts are a useful addition. They also provide an extra layer of warmth. Jackets have pockets but if you use a backpack, as I do, those pockets are often hard to get to because of the backpack hip strap. As it gets colder I switch to wind proof pants over merino wool long underwear. I prefer long underwear to bike tights because when I get to work I change into a pair of pants, and long underwear is more comfortable under pants than bike tights.