I'm far from Alaska so my riding conditions aren't nearly as extreme as Jill's. On the coldest winter nights it might drop down to the minus single digits Fahrenheit (about -20 C). At those temps my typical wear from top to bottom is:
REI Obnoxious Yellow cycling shell jacket with midweight fleece shirt,
insulated ski gloves,
lightweight fleece pants with a windproof shell over it,
midweight Bridgedale hiking socks,
plastic baggies over the feet to block the wind, and
Lake mountain bike shoes.
When it's that cold I'm not out for a recreational ride. You cannot get enough air into the lungs quickly enough to get a meaningful workout when it's far below freezing; it's better to stay indoors and hit the rollers or get some weight training in.
When I lived in Illinois with winter temps at minus 20 and the prairie wind blowing at 20+ mph, I wore two pair of heavy wool army socks, black leather army boots, and approximately a zillion layers of heavy army surplus covering my legs and torso.