The heat that is within your body is the most valuable and beautiful resource you have when city running in winter. It is precious and harnessing it efficiently without negatively impacting your mobility is the key. All is concrete and absorbing the cold. Wind will already be a factor, but the faster you choose to carry yourself the more defeating the wind can appear. You will feel the need to fight against it, but as long as you know and feel your own body's warmth through and through, there is no competition.
That isn't to say that you're safe running around in the nude screaming 'MY BODY IS A GOLDEN SUN EMANATING THE LIGHT AND THE HEAT TO WARM THE COLDEST OF SOULS.' You will get stopped, and you will put yourself in danger. There are many sorts of light weight insulating layers that work with your body's heat to effectively provide a second layer of skin while helping manage the danger of your perspiration pooling and making you colder. I personally use Uniqlo's line of Heattech apparel, which is a unique composite of rayon, acrylic, polyurethane, and polyester. While the classic and most traditionally effective winter warmers are made of wool, or a wool/cotton blend, Heattech is my go-to because of the light weight, low cost, effective insulation, moisture management, general softness, and lack of nipple irritation. I cover my upper body in that while my lower body looks nearly identical to how it would during warm weather running.
The extremities and the head are the areas that one must be most concerned about when it comes to loosing body heat, or experiencing extreme pain due to lack of ample blood flow and tons of nerve endings. I take what most might consider a 'rugged' approach to managing my fingers and toes, and it won't work for everyone but take note if you'd like. Forgoing gloves, I stretch the Heattech fabric over my hands and keep them in a clenched fist through most of my running. This keeps the fabric in place and my fingers huddled together, working as a team to retain as much heat as they can. If they are feeling particularly cold, exposing and pressing them against the cheeks of my rear-end is a lovely quick blast of warmth, from me to me. My toes are still in Vibram barefoot wear (haven't quite talked much about that yet), and they will certainly be far colder than they would be during the summer. The kinetic energy and blood-flow of my constant motion is enough for them to find a comfortable enough equilibrium, which may speak to my personal pain threshold. On my head I will either have a beanie hat or a simple set of ear-warmers depending on how cold it is.
*****MEN PAY ATTENTION*****
The genitals are an extremity. Though this already occurs during general running, in the coldest of temperatures the bag full of future humans will retreat very far in to the body, as will the distribution tube. If temperatures drop well below freezing, one must provide that area with extra insulation. Thawing out and regaining feeling in the mushroom tip is FAR more painful than the same sort of thing applied to fingers or toes. When necessary, I wear a pair of compression shorts under my regular running shorts and toss a balled up sock down there to block the wind and keep the little guy a bit warmer. It has nothing to do with me feeling inadequate...
*****WOMEN RESUME READING*****
Let's talk about snow. In this city it is only briefly 'pretty' and will very rapidly get packed down in to uneven masses, turned in to cold slush, or eventually freeze over entirely. Combine all of that with the fact that the colder temperatures will naturally decrease your reaction time and you now must respect the situation and run differently. You are not going to be able to stop as quickly or turn as sharply and the same applies to all cars on the road. Everybody's traction is depleted and this must be taken in to account. On top of that the air will likely be quite dry and exposed skin/lips will easily clam up or get irritated. Keep the chap stick handy and maintain a habit of moisturizing your skin regularly as you might already during the season.
So with all the heightened danger and discomfort, why would I (or anyone) want to run out there in it? The short answer is that I love it too much to let weather stop me, but there's a longer answer. In winter, running takes on a beautiful urgency. The body recognizes the conditions and the act of keeping it in constant motion, raising the core temperature slightly, becomes about survival. Dealing with snow/slush/sleet/ice forces engagement of the muscles responsible for balance and stabilization just as much as the muscles responsible for propulsion; every step taken with care, focus, and calculation. IT'S AWESOME. You'll continually marvel at what your beautiful mass of bio matter is capable of through powers of adaptation. It's about basking in the thrill of being alive. It's about not allowing the state of your environment to purely dictate how you move through it. It's about deep appreciation of the contrast present when you find your point B and get all cosy, well beyond the simple thinking of 'thank heavens I'm finally out of that dreadful cold.' Be safe, have fun out there, and remember the most important phrase in winter running: never stop.