Really cold: Two pairs of thin running tights work just as good as a thick pair, sometimes I think even better.
Show: IceBugs shoes. These are more like trail running shoes but with steel tip springy spikes in the bottom, great for running across even the slickest ice and waterproof too.
Smartwool ski/snowboard socks
Lightweight gloves underneath mittens when it’s really really cold
On top multiple thin layers, for me I’ve put on up to 4 or 5 layers

The balaclava works pretty good though in the coldest of weather I’ll wear a ski mask/hat combined with the balaclava

Those disposable handwarmers. When it’s near zero with wind, those make all the difference in keeping your hands warm

In the most severe weather, I’ll throw on tights and a long sleeve, and over that put on a triathlon suit so you’re covered from head to toe with no chance of wind getting in and then layer over the top of that.

Cold weather running can be a lot of fun as long as you’re prepared for it.

While I’m not ready for snow just yet, I can’t wait for the first run in the snow.

Pair all of the above with ice spiked tires for your mountain bike and you can pretty much do just about anything no matter the weather conditions.

-John
(totally a non-runner)

- Stocking cap that allows heat/moisture to escape from the top (I just wear a nice North Face cap)
- DriFit t-shirt (Wick that sweat away)
- Asics Thermopolis® LT Half Zip (Get one of these!)
- Tights (Not the thin crappy kind but the nice kind with zippers. I think I wear Mizunos)
- Nike Lightweight Running gloves (Anything too heavy will cause your hands to get way too hot)