Balaclava for your head
Winter boots for your feet or booties for your bike shoes
Mittens not Gloves
Avoid cotton.
"Merino" wool socks from Costco
Wicking base layer
Fleece warmth layer
Wind proof outer layers
Ski goggles when it's really cold

Studded tires are for ice and hard packed snow. They do nothing in loose snow.
Knobbies help in loose snow, but the best trick is to run your tires at low pressure.
Don't turn fast or expect to stop fast.
Some people go clipless all year but I prefer platforms in the winter.
I'm not one to claim that fenders are a must but in Winter I really really recommend them.
It's darker in the winter so lighting becomes more important.
Put a light coating of oil on all the unpainted steel parts of your bike to help keep corrosion at bay
Plan on having to clean and lube your chain a lot more often.