I’ve done winter commutes in DC for 3 years now, albeit much shorter distance.
My normal commute is in office clothes with the following additions for cold weather
1) winter/warm boots with wool socks (smartwool or darn tough are my go-to)
2) merino wool base layer on the bottom
3) Warm winter coat (I really like my Land’s End Squall – it’s warm and fuzzy on the inside and water/wind blocking on the outside with elastic cuffs and a full throat zip up)
4) Buff or neck gaiter
5) Ski goggles
6) 180s ear warmers+bike helmet
7) “Lobster” gloves
Most cold days in the office I’m wearing a merino wool V neck sweater over my shirt and tie anyways, so that’s part of my warm commute
If it was colder or I was doing longer distance I would add bar mitts, a real balaclava instead of the buff+ear warmer, a 2nd pair of socks, and some sort of wind/water resistant pants.
I’d suggest buying cheap stuff off Amazon or TJ Maxx or something and replacing it with better stuff as you decide what you like or it wears out.