Luckily, most cold-weather cycling gear also works well as cold-weather running gear( and xc ski wear).
High 20s to high 30s I usually wear thin tights, a sleeveless base layer (e.g. UnDeeshirt), long sleeved base layer, windfront vest, magic-finger gloves, wool socks and a fleece earband.
When the temps drop below low 20s and/or there is severe wind-chill and/or precipitation I'll wear: heaver tights, a second ls base layer, full shell, mittens (wool socks work in a pinch) and either a full ski hat/neck gaiter combo or a balaclava.
I really like my short, waterproof gaiters from xc skiing when I run in deep snow. It's nice to have warm DRY socks!
I find that my trail-running shoes provide more grip on slick surfaces. They also provide more protection from the elements (not as much mesh). I bought my last pair 1/2 size larger so that I can wear nice thick wool socks.
Oh and if you have easy access to trails, I'd much much rather run in the woods in the winter. Great wind protection.



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