Hi Sortabadass (love your user name!)
I am in the same boat. I am currently running 3 times per week, 5K each time, except sometimes on Saturday mornings I do 6K. I am loving it! I live in Canada so we get a ton of snow here. We also have an amazing snow removal system in place so after a snow fall, there is usually only one, or on occasion 2 days, when it would be impossible to run outside.
While I have never run in the winter time, I have power-walked. Basically I purchase "winter" running shoes. My preference is the Asics Gel Trabuco. They have amazing support and cushion and have treads underneath to prevent slipping. Here is a link to the Asics site. ASICS America - Running - Women's Footwear - GEL-Trabuco® 13
Also it's important to get the right clothes. Be sure not to wear cotton as that will get wet when you sweat and not wick the moisture away from your skin so you will get very cold! I like Under Armour clothing. Under Armour® Performance Clothing, Shoes, and Accessories - Free shipping available
Be sure to layer and not overdress as you will sweat and even overheat. It's best to have a fuel belt with you too, so that you can stay hydrated.
All of these things cost a little but I have had my Winter gear for a few years so it's a great investment.
Here's a great article about it. Cold Weather Running - Cold Weather Running Safety Tips