How do you stay warm if you have to work outside all day in this frigid weather?

The following links will help to explain in further detail regarding dressing for extream cold.

Extreme Cold: A Prevention Guide to Promote Your Personal Health and Safety
http://www.bt.cdc.gov/disasters/winter/guide.asp

Hypothermia
www.hypothermia.org
Frostbite
http://www.mayoclinic.com/health/first-aid-frostbite/FA00023
Frostbite Prevention.
http://www.stjohn.org/TraumaCenter/Prevention/frostbite/

In general, the rule of thumb for living in a cold environment
is to get lots of insulation between you and the
environment, and to remove that insulation layer by
layer when you get warmer. You need a clothing system
that allows you to shed layers quickly and easily before
you get damp from perspiration. Several thinner gar-ments
will serve this purpose better than one bulky
overcoat.

Long Underwear: Your first layer should be
your long underwear. It should fit snugly against
your skin and be made of a nonabsorbent mate-rial.
This layer works by wicking away water
and keeping your skin dry. Synthetic fabrics
such as polypropylene work the best, whereas
wool and silk are the best natural fibers. Cotton
is a poor choice because it absorbs water and
holds the water next to your skin where it will
cool you off.
• Mid Layers: The next layers are important
because they serve to absorb the moisture out of
your long underwear and transport it to the
environment through evaporation. Once again,
synthetics are best here, but wool is a good
substitute. Shirts, sweaters, and trousers are
what you will likely be wearing when you are
active. Pay close attention to the fit, as the mid
layers work by trapping air and preventing it
from circulating and carrying away your body
heat.
• Insulation Layer: Thickness is warmth. For
sedentary activities or extremely cold condi-tions,
an outer garment with several inches of
loft is recommended. Down, Polarguardô,
Holofillô Thinsulateô and Primaloftô are the
types of insulation that the USAP uses in the
ECW gear. For personnel working in the Penin-sula
area it is important to understand that down
loses most of its loft when wet and takes a long
time to dry, so you must be careful to avoid
getting down garments wet. Synthetic insulation
is a better choice for working in potentially wet
conditions.
• Shell Layer: The most important part of your
layering system, and the most used besides your
long underwear, is your windshell. Studies
conducted by Recreational Equipment Co-Op
show that in still air, windshells worn over any
garment can add up to 25 degrees F of warmth.
In windy conditions, windshells can increase
warmth by 50 degrees F or more.
Personnel working in the McMurdo system are
issued a windshell that is windproof but not
waterproof. Because of the dry climate, the non-waterproof
fabrics are superior because they
allow your perspiration to escape more easily.
Personnel working in the Peninsula area are
issued a waterproof/breathable windshell be-cause
of the potentially wet conditions encoun-tered
there.

More on WINTER WEATHER SAFETY
http://www.nws.noaa.gov/om/winter/index.shtml
http://www.disastercenter.com/guide/winter.html
http://weathereye.kgan.com/expert/blizzard/WinterSafe.html
http://www.redcross.org/services/disaster/0,1082,0_595_,00.html
http://www.semo.state.ny.us/info/publicsafety/winter_safety_tips.cfm
NEW and OLD Wind Chill Chart
http://www.srh.noaa.gov/shv/windchill.htm
http://nsidc.org/snow/avalanche/
Extreme Cold: A Prevention Guide to Promote Your Personal Health and Safety
http://www.bt.cdc.gov/disasters/winter/guide.asp.

Wear thermal underwear, keep moving, jumping up and down, etc to keep your body working. If you keep your body moving, you'll keep somewhat warm. Wear a hat, something that covers your ears, thermal gloves, two pairs of socks, and heavy boots. Dress the same as if you were going skiing or snowboarding.

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ive work outdoor most of my life layers of what ever you have.... feet and hands and head are the most important.... and they make things to help ive used hand warmers with a couple gloves rubber boots are warmer than leather in most cases and for headware nothing better than a wool

Wear thermals - longjohns and long sleeves. Keep as dry as possible. Wear wool clothing. Use wind (and rain) proof outer wear.
If you are standing in one spot, then stand on bubble wrap, carpet or polystyrene.
Wear boots and put wool or felt inside. (you can get lambs wool linings).

Have a thermos of a warm drink, slightly warmer than body temp, but not too hot. Try and avoid getting too sweaty.

Go inside if you can, or at least keep out of any wind draught.

Layers, Layers, Layers.

layers. A couple layers of socks. 3 shirts under my hoodie. and a very warm hat, scarf too. Gloves and probably underarmor legs under my pants

I think the Packers and the Giants may have some advice on that one for you.
I've done some outdoor tailgating in this kind of weather myself . . .those little things you put in your gloves are AWESOME to keep the hands warm. They have the for feet, too - or you can use the hand warmers and put them in between 2 pairs of socks.
I find that going to the outdoor sporting stores is the best place for warm weather gear - and ideas!
(like Gander Mountain Sports)

Stay dry dress in lots of thin layers

Layers, layers, layers. Also check into Carhart Brand outerwear.