Others may disagree, but my opinion is that if you are doing hills in the winter, you should have studded tires. This is doubly true if you are on the road and not on separated bike paths; your life is worth more than the $100-$200 for a high quality set. I went one winter without, and even in relatively flat Madison WI saw a marked improvement in safety when I switched to studded tires.

The other thing you need for winter riding (on your bike) are good lights, front and rear. I run two each; one set on my bike, one on my helmet. That way, if I wipe out, there is still a good chance that a car will see me laying in the road and stop.

Otherwise, I think your bike should generally be ready to go. You can add useful accessories like fenders or go single speed (though with vertical dropouts, you will still need a chain tensioner unless you go to some interesting solutions), but these are less critical than good clothing. You will learn what you need/want; each person is different.