I ran outdoors all last winter (and I live in IL where it gets pretty darn cold!) & my one recommendation is to get a good pair of running tights!!! I got mine at a local running store, but you can get them online also. Mine are Nike & they kept my legs sooo warm but also are dry-wick so I didn't get cold. Some days when it was close to or below 0 I'd put another pair of pants on over them. Also, anything dry-wick for shirts are great- I would layer a sports bra w/ a long sleeved shirt & if it was really cold then I'd put a fleece on over it. You can wear a hat or fleece wrap for your ears & of course gloves!!! Also, my running shoes are vented so I'd wear one pair of thin dry-wick socks & then put a thicker pair of socks over them.
ETA: You can get some really good cheaper dry-wick stuff at Target, Kohl's, or JC Penney's if you don't want to spend a lot of money on name brand Nike or Adidas.
I love running in the winter, especially when it's snowing!!! Good luck!