I bike in Seattle. A lot is going to depend on your commute length, facilities on both sides, and how far you're pushing your commute. Most of the winter is overcast and showers, not pouring rain. It's also not usually that cold (30's to 40's).

I typically wear merino wool top/bottom from Costco (depending on temperature), Showers Pass Elite Jacket (very popular around here and works really well), and biking tights. For heavy rain days, I have Pearl Izumi WxB pants, but they really don't breathe well so I'm not a big fan. I'm looking into softshell pants right now to replace by bottom half clothing for all but the rainiest of days.

For gloves, I use PI WxB gloves. They're expensive, but they work well. You can also probably get their softshell gloves - just make sure they have some amount of weatherproofing.

I've found shoe covers don't work that well for me below 40-50 degrees. When it's cold and wet, they just don't provide enough coverage or heat protection. I invested in Lake boots (MXZ303) which are much much better, simpler to put on, and keep me both dry and warm. They're probably meant for even colder conditions, but they're fine into the 40's and 50's as long as you vary your socks accordingly.

No reason to buy studded tires here. If it ever snows, shelter at home and hope no car hits your building. People here can't drive in the snow. Black ice is a bigger concern, so be careful. Studded tires are definitely not worth it for that though.

Make sure you have fenders though.