Although I've run off and on for over 10 years, this is my first winter of dedicated training. I've found that dealing with the cold is not too bad--there's other factors that make winter running more difficult.
Up here in the North Country, there's about a month where winter running is difficult because of the limited daylight hours. It's dark when I leave for work, it's dark when I get home from work, and I'm not going to run outside in the dark. I know there's people who put on an LED headlamp, reflective gear, and even those who carry a flashlight, but I'm not that kind of person. First of all, no matter how much reflective gear I wear, it's not going to keep me from getting hit by a car. There's very few sidewalks in my neighborhood and I don't really trust people to see me even if my jacket and shoes are reflective and I'm wearing some LED headlamp.
Secondly, if I'm wearing all that reflective crap, I've just made myself an easier target for would-be muggers or those looking to assault a runner just for the rush. At the end of fall I was doing some running just after dark and I passed two young men, one of whom uttered loudly, "What the f---?!" in a threatening tone that made me feel less than safe. Fortunately, I was running and they both had their pants hitched up to their knee caps, so unless they were going to shoot at me I was OK.
The other major problem with winter running is where to run. I like to find routes that have good footing, and that's not always easy in the Twin Cities. I've got a pair of homemade screw shoes, as well as some YakTrax, but both of those have some problems, especially where I run. The YakTrax do great for packed snow and unpacked snow up to about 2" while the screw shoes do pretty well on packed snow and ice that's a little broken up or melting. The problem is that most routes have a variety of surface conditions that aren't optimal for either the screw shoes or the YakTrax.
I find the YakTrax don't do so great on ice and the screw shoes are pretty worthless for unpacked snow. Both have problems on really thin sheets of ice--there's not enough for the screws to dig in and the YakTrax just slide all over the stuff, leading to falling down at a four-way stop whilest people laugh at me from their cars. The screw shoes are OK for regular pavement but the YakTrax are uncomfortable and lack traction when the pavement's clear of snow and ice. I probably look like a moron when I'm running--moving back and forth on the side of the road or the sidewalk to stay on the snow-packed sections.
The funny thing about winter running is that the cold doesn't really bother me at all. As long as I dress in layers I stay pretty warm. I put a little petroleum jelly on my face, wear a hat and gloves, and I'm good to go. I've seen people in ski masks and all that but my face really doesn't get that cold. I do tend to form sweat icicles (or sweatcicles) on my beard, which make me look totally awesome.