I am not a fan of cold weather in general. I wear layers - I mean two pairs of pants – at least December through February and often longer. Yet, I discovered last year that I really enjoy winter running, maybe even more than running in the summer. Running in falling snow is beautiful and peaceful. Since your body is working more while jogging, I’ve found I am more warm than when I walk the dog wearing more layers and heavy clothing. My friend just purchased some Lululemon gear he says is extremely warm; I would love to review it for you, but it is outside my price range. Luckily, it should cost very little to outfit yourself to run all winter long.
The best place to start with any running list is the shoes. I wear regular running shoes. You will just want to ensure that they have sufficient support and traction as you will likely be running on slick or uneven ground. If you run with your dog, you may want to leave him or her at home unless they are well-trained or unable to pull you, or you may end up being pulled off your path due to the slick snow or ice. I have run a 5k with a Great Dane, but he outweighs me and is too excitable for more than winter walks.