The biggest thing to note, if you're properly dressed is that most of the effect is on your head.
Remember, first of all that
"There is no such thing as bad weather, only bad clothing."
When you've got enough layers on you should be plenty warm enough. In my case that means
- Feet : 2 pairs of thin socks, inner soles and boots
- Bottom Half: long underwear, pants and trousers
- Top half: thermal T-shirt, lumberjack type shirt (cotton blend), jumper, wool gillet and coat
- Head and neck: elasticated tube scarf, wooly scarf, corduroy hat
- Hands: wool gloves - if you have long wrists on them and your hands get cold just pull your fingers out of the glove's fingers and get your whole hand in the palm section
A hat which goes over your ears is pretty much essential as if there is any wind you're going to have bright red ears after 10 or 15 minutes which can be pretty painful.
Your nose is pretty easy to warm up - just put your hand over it! The oddest sensation of the lot though is your nose freezing from the inside out. The moisture in your nose freezes making your nose go stiff and feel very dry. It is a very odd feeling not really painful, just weird.
Below minus 20 is somewhere I haven't spent much time (not since being in Moscow in February - I think in '97). From what I remember, a second pair of gloves - or big pockets is a great idea. You did see an awful lot of fur hats and coats at the time too. I also had problems with my breath making my glasses freeze.
There you go - just thought the cold snap made it a good time to post this with a severe weather warning due to cold in Britain and many people no doubt unprepared for it. I remember seeing people in jumpers without coats wandering round when it was 2 or 3 degrees over Christmas - not something bright to do in the minus temperatures!