Frequently lubing your components (especially your chain) is crucial in cold weather. Lube (which won't freeze) pushes out water (which does). Besides the protection against freezing, it also will help extend the life of your components even in the face of sand, salt, and gravel debris from cities deicing the roads. Fenders with mud flaps are useful as well, as they will protect your drivetrain from slush. Basically, anything you can do to keep the bike's componentry dry is crucial.
To this end, I would bring the bike inside overnight every day in order to warm it up. This lets water drip off of it, and you can wipe off any that's left with a pile of used rags before you take it on the road each day.
The temperature flux might cause wear on the components, but I suspect the amount pales in comparison to the damage done by freezing (ice expands, putting pressure where it shouldn't go), salt (which corrodes steel), and sand (which prematurely wears components due to grinding).