Here's what Mother Earth news says:
What the Cold Does
Cold weather makes the engine hard to start for two main reasons. First, oil thickens when it's cold, which increases friction and makes it harder for the staner motor to spin the engine. Cold also slows the chemical reaction in the car's battery, reducing its power output. Battery output is usually rated at 77 degrees Fahrenheit, below which starting power drops drastically. As shown in Figure I, (See the car diagrams in the image gallery) at 5 degrees Fahrenheit a fully charged lead-acid battery has only half its rated amp-hour capacity. You can ensure that your car will start in the worst weather by keeping the engine or the battery, or both, warm. But before we discuss some of the ways - short of building a heated garage - to keep the underhood cozy, let's review basic maintenance.
http://www.motherearthnews.com/natur...z87jfzgoe.aspx
So to answer my question, both oil and battery need to be kept warm.