I think it is important to think about what you are wearing before what you need to do to your bike to ride in the winter. An improperly set up bike will survive to be ridden another day, the same cannot always be said for the rider. That being said I'll start at the bottom and work my way up, because that is where most new winter cyclists (and even some experienced ones) have problems.
Feet - The question for the ages, clipins or platforms? If you don't normally ride clipped in, this isn't probably a real question for you. You can use regular platform pedals and some huge pack boots at the worst and be just fine. You may want to consider a set of Power Grips. While many people are just fine with platforms, it can be hard to keep a big set of packboots on the pedals, and Power Grips solve that problem nicely. Now, if you are like me and refuse to give up being clipped in, there are only two options in my mind. Make something yourself (see duct tape, screws, superglue, and ruining your set of packboots) or buy some Lakes. I actually have two pair. One set of size 46 (I normally wear a size 44) to wear down to -10F and a set of 50 wides to wear down to whatever it gets down to. If I could go back in time, I'd buy the 46s in wide too, but I don't think Lake was making wides when I bought them, or maybe my shop just wasn't carrying them. Like lots of other things in life, wider is better. Give yourself room to pack in a couple pair of socks. If you don't by loose fitting footwear, when you do start stacking in the socks (read insulation here) you'll just end up mashing your foot into something that will constrict the blood flow and actually make staying warm harder. Air space is insulation. If what you are wearing feels tight, that means it will affect your circulation, and that means you will get cold easier. I really can't stress this enough. I also choose to use a vapor barrier sock. Specifically one made by Sugoi. I have been trying to get my riding buddies to use these, but they just keep looking at me like I am crazy, so they are probably not for everyone. Personally I think it gives me another ten degrees out of the same setup. I looked for a site with a good explanation of why VB clothing is good and the nearest I could find was this. It is a bit militant, but you'll get the picture. Finally I have a warning. If you are riding and your feet get cold, get off and walk or run. The friction produced by running/walking will help warm up your feet. The joy of riding really isn't worth losing toes over (well maybe, but still get off the bike if it comes to frozen feet).
Baselayer - For baselayer I recommend wool. The brand I have the most laying around of is definitely Ibex. I see several advantages with wool, sadly none of them cost. The first is the love of my coworkers. If you commute day in and out, it is highly likely that you won't be washing your cyclewear daily and won't have enough to switch to new clean baselayer everyday. Wool can withstand this kind of abuse without producing noxious odors. That is just what it does. Sure there treated synthetics that supposedly don't stink. They might even work. But I am a wool fanatic, so I won't be trying them anytime soon. The second reason I love wool is that I think it keeps me warmer when damp (like soaked in sweat damp) than the synthetics I have tried. Just my observations, which I will treat as fact. I keep my synthetic stuff around for nonaerobic activities and day trips in other sports, when I ride and it is cold, I will be in wool.
Legs - This is an area I tend to deviate from most other cyclists on. My legs get cold very easily. What I consider necessary wear, many other spinners overheat in. So consider any recommendations I make to be on the warm side of the spectrum. When it drops down to 50F or colder, I wear tights. My current favorites are the Firewall 220 bib tights by Sugoi. These things are warm, if I put a pair of wool tights on underneath them I can comfortably get down to 10F or so. Many people I know can ride them much colder than that. Pearl Izumi also makes some very decent tights, but I find the Sugois to be a bit warmer and have a thicker (and thus also warmer) chamois. When it gets colder than 10F I go to a insulated pant. Currently I am using a set of Patagonia micro puff pants, which apparently they aren't making anymore, because I couldn't find them on their website. I did find a picture here. Mountain Hardware and a couple other companies make similar products. They are reasonably expensive and warm as all get out. Expect to patch the inside of your drivetrain side cuff soon after getting them.
Torso - Here again I seem to deviate from the norm. What my legs seem to lack in heat generation, my torso more than makes up for. I rarely wear more than two layers. Never more than three. Again with the Sugoi for an outer layer. Have I mentioned that I tried to have Sugoi's love child, but they turned me down? Under that I wear a Ibex shirt (sadly also turned down by Ibex). Depending on temperatures, I'll wear a microfine base layer, a midweight shirt, or in real cold temperatures (below -25F) a Shak. That's it. In super cold temperatures (-35F or colder) I pack a lightweight down jacket in case something happens and I need to stop for a bit, but I have yet to actually need it.
Head - Many cyclists try to wear a bicycle helmet in cold temperatures. While I applaud them for trying to be safe, I also think they are silly. Many companies make helmets for winter aerobic activities. Giro comes to mind, mostly because I am rocking one nearly daily. With the add in speakers I can have warm ears and be totally oblivious when someone in a car recklessly tries to run me down. For a facemask I use a Pearl Izumi (again either not made or no longer listed on their website) or when it gets really cold an OR Gorilla mask. The mask serves double awesome duty by consistently forming two long icicles on the front during super cold weather which end up looking like wicked cool fangs. I don't wear goggles. I know a select few people who wear goggles and make them work. Mostly I guess they are genetic mutants who exhale no moisture when expiring. If you find the perfect setup for them and like it, they will keep your eyes warmer. However, most people seem to endlessly mess with them and end up with a fogged, frozen mess by the end of a ride. My eyes seem to be fine while riding, even at subzero temperatures. I have had my eyes freeze shut on occasion, but an application of a warm finger generally fixes that. I would guess that on average, I have to defrost an eye less than once a ride. I consider this better than the endless mucking about I did with goggles before I finally stopped trying to use them.
That is pretty much it. While I didn't mention hands, I recommend your favorite summer full fingered cycling glove. If you want to ask how that could possibly work, please see my post on bicycle setup, and hopefully your questions will be answered. I normally ride with a pack (currently a Gregory Advent Pro), which conveniently is no longer on the manufacturer's website either. While some folks prefer panniers, I prefer to be able to dynamically move as much weight as possible, which means it needs to be attached to me, not my bicycle.