I've said it before; I'll say it again. "When acid rain freezes, you get acid snow"
In fact, in South Jersey, thanks to Climate Change, we don't even get 'treacherous icy death' nor 'soft fluffy stuff' anymore. We get a semi-frozen semi-corrosive slurry, covering rocks and sand and gravel and shoes and needles and underwear and little bottle of Fireball and hubcaps and roadkill and all sorts of other shit. When that all dries out, the slush is gone, but all that other crap is still out there, usually migrating onto the part of the road I'm using, and collecting in any number of brand new potholes
But I digress ...
Winter Training is
especially Badass, and Outdoors is doubly so, but there are couple things to keep in mind
It's usually dark in Winter, so you want to see and be seen as best as possible. I run with a reflective vest, safety neon shirt if it's warm enough, reflective gloves, and a red clip-on strobe in back. I have LED headllamp to light the way up front. If you're on the road, run FACING traffic so you can see the headlights long before they see you and NEVER EVER wear headphones ... if "NO headphones" is a deal-breaker? Get back on the treadmill
As important as traction is, remember this: Dry = Warm, ESPECIALLY your feet.
Everyone says you lose a lot of heat off your head, so wear a hat BUT, if you accidentally step in a puddle, and your feet get wet? A cold noggin will be the least of your worries. You'll get home & shower and dry your hair and that will be fine; but cold damp feet just seem to linger and make you miserable HOURS afterwards. If there is any dampness outside, I put on my socks, slip some bread bags* over them then put my shoes over those ... function > fashion, here
* you could use any plastic bag I guess, but I like the long skinny ones that bread comes in
"What's your claim?" - Ben Gravy
"Your best work is the work you're excited about" - Rick Rubin