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I ran every day in the winter for many years when I lived in New England, often on trails since the roads were salted either became a slushy mess or very icy. Down to -20C or so, polypro-lined running tights, a polypro shirt, a fleece midlayer, a windbreaker, and gloves and a hat were sufficient. Never used plastic bags or gaiters for my feet but I did have three pairs of running shoes and many pairs of synthetic socks, and rotated them so that I always ran in a dry pair. If it was colder than -20C or very windy I'd make sure I had something over my face (scarf or balaclava) to keep it from getting frostbitten. I really liked running in fresh snow in winter because it was very quiet and there weren't a lot of people out, and you could regulate your layers so you don't sweat much. Of course if you are going to run alone on a trail where there aren't other people and you can't easily bail out to civilization, it's a good idea to bring extra layers in case you sprain your ankle or suffer some other injury that might force you to walk or limp out.

If I'm doing local trail running and familiar with my surroundings, I'll generally need nothing more than running shoes, tights, long sleeve shirt, windbreaker, thin gloves, and a hat. I did a run of the Thunderbolt Trail on Greylock, MA, the other day and there was around three inches of snow on the top with 25 degree F weather and high winds. I had a long sleeve shirt, shorts, hat, and shoes on, and it was very cold, but gloves and a windbreaker would have made me plenty comfortable in that sort of weather. When you're keeping a good pace (mine is around 7:00) for anywhere between 5-8 miles, you should heat up fast enough to need nothing more than this. You can start with an extra fleece and tie it around your waste once you warm up.

If you're running somewhere you're not familiar with, I will try and pack a Cliff Bar in my pocket, always an extra sweatshirt, and gloves. The pockets in a windbreaker are good for bringing just about anything you could need (i.e. cell phone, food) if they have a zipper. Have a good time running this winter - pb

It would have to be damn cold for me to do a vapor barrier in my shoes while running. I use them in the winter while mtb'ing, but that's because my clipless shoes are extremely ventilated and the speeds are higher so my feet get cold as hell. While running, I've never had that problem, even running down to -4F. I don't tend to run through much standing snow though.
Depending upon how cold it is, you may want something to cover your mouth that you can breathe through readily. It will soften that cold air a bit on your lungs.
Personally, I tend to have more troubles with overheating than anything else, but a big piece of the puzzle for gear, as others have noted, is the sort of location you're planning on running. The more isolated, the more ready for weather changes you need to be, so the more you'll carry. If it's not terribly isolated, I'll wear a silkweight ls capilene, lightweight beanie, liner gloves and shorts. This suits me down to about 30F if the sun is out. If it's overcast or breezy Istep up the thickness of my ls because that will still breathe well, and I may don tights. If I'm getting a bit off the beaten track, but not too far, I carry a lightweight softshell which I can strap to my Camelbak. I have the older version of http://shop.camelbak.com/2012-ultra-lr-vest/d/1070_c_131_cl_585 which doesn't move at all and isn't annoying to run with.