1) The "feels like" temperatures. This is another way of peddling the "wind chill" nonsense that weather guessers have been hyping for so many years.
Here's the more brutal truth: If you're from a warm location, where you've never seen or experienced sub-zero temperatures, and you take someone like me, who has previously lived and worked in areas where it got down to -45F in the winter... there's no comparison in what we're going to say it "feels like." If you're from Florida (that's just an example - you don't say where you're from) and we're standing outside in -20F temperatures and we're both dressed just about the same... relatively speaking, you're going to be miserable and say "it feels like..." and you'll have no basis for comparison.. And I'm going to be thinking "It feels like XXX, and if I feel cold, I'll be telling myself 'I've survived far worse... this isn't that bad.' "
I've been out in enough sub-zero temps to be able to tell you within a few degrees just how cold it is out -- with or without wind - from the sound of snow under my boots, what falling snow sounds like, how the hair in my nose is freezing if I breath through my nose, etc. There are all these little clues you can pick up on as you gain experience in sub-zero temps that give you an idea of how cold it is.
Once you adapt to the cold, you'll likely deal with it pretty well too. Figure on a six months to adapt if you're from someplace where it gets down to 0F, and a year to adapt if you're from some place where it is warm all the time (like, oh, Florida or San Diego).
2) Now, speaking as someone who has been in -45F temps, here's what I have to say about winter temperatures: once you get acclimated, temps down to, oh, -10, maybe -15F, aren't that bad. Really.
You're not going to want to go out on the back deck sunbathing in a bikini (unless you want a standing ovation from the neighbors, who will make sure the rest of the town knows you're the "tough chick who sunbathes in sub-zero temps"), but -10 to -15F is something that you can deal with if you work outside if you have on the right clothes and something you can stand in ordinary street clothes for a little while as you move between buildings, your car, etc.
Depending on the person, somewhere between -15F and -25F, it quits being merely chilly and gets to a point where most all people agree it is cold. People from Florida go catatonic, people from Minnesota and the Adirondaks say "It's kinda nippy out today, dontcha think?"
At -35F and lower, there is no humor in the situation, and at temps like -45F, you never grab onto bare metal with your skin, you think very carefully about everything you do in terms of consequences and the quality of your clothing starts to make a very real difference, in particular your gloves, boots and what you're wearing on your head. Cars often don't start worth crap. Diesel engines are almost useless unless they're kept indoors or have been specially equipped to pre-heat them.
My experience at -45F taught me that the rubber gaskets on things like car doors, some household windows, etc -- freeze to the metal. You can't open some car doors at -45F, much less get inside to start the engine. Your tires get a flat spot frozen onto them, and for the first few miles you need to drive slowly to allow the tires to "get round" again.
At deeply cold temperatures, if you're working outside, what you must think about more than warmth in clothing is how well you can get rid of water vapor from your layers of clothing. You can have the best, warmest layers on when you start out the day - and if you're wearing some water-tight shell on the top layer, and the water vapor coming off your body (ie, sweat, transpiration) does not have some way to get out, you're going to end up a sodden, frozen mass at the end of the day.
Wool clothing does well at letting out water vapor. Wool also keeps you warm even when wet. Gore-Tex is noted for allowing water vapor out, but it can get brittle in really harsh cold. Nylon shells... I avoid them like the plague.
3) What Brian said about beards - they do help, but really only in the wind. The fine "peach fuzz" that women have on their faces does almost as much as a beard does. What hurts like heck is when I was young and I'd shave every morning for work, then step out into -20F temps with even a slight wind and a bare, newly shaved face. There is no pain quite so difficult to explain to those who have not felt it as this. It is like getting shaved all over again with the finest German steel straight razor that is on fire as it glides across your face.
Even only one day's worth of stubble solves the issue. All you need is the slightest bit of fuzz to break up the wind flowing over your skin. I don't bother to shave any more, and as Brian says, I don't notice that it is any warmer in the winter or hotter in the summer. It's just fur that stays trimmed, that's all. Getting it full of rime ice in the winter tho, means I have to wait for my beard to melt sometimes before I can eat after being out in -10F or lower temps.
So, since I'm guessing you don't shave, it probably won't be a problem. But since I'm guessing you do have hair on your head, allow me to offer this: don't go stepping out into -20F or colder temps with damp or wet hair. In really cold temps, your hair will freeze and if in really cold temps with really damp hair, it can break off.
Dry hair is a Good Thing in cold temps, no matter how much hair you have. Wet hair means you're losing a lot of body heat out your head area.
4) -40F and lower temps and clothing.
Well, you need a good set of pac boots. Here's some representative boots; this isn't a recommendation to buy from this vendor or for the products, just that they have a list of various temp ranges:
Drew's Pac Boots
If you were really going to be working consistently in -50F temps, then you need to go to something better, like bunny boots that are used in Alaska. The bunny boot is white, and is constructed a little like a thermos, with an air gap between the inside and the outside. You find bunny boots in military surplus dealers.
Wear wool socks. Make sure your shoes/boots don't bind or restrict your blood circuclation in any way.
In sub-zero conditions, you generally don't want to use gloves. You want mittens. Mittens keep your hands far warmer than gloves. I have deerskin mittens that are lined with removable wool liners, and then I have polar expedition weight mittens for hunting from a company called "Northern Outfitters:"
4 Piece Mitten Set
I have and use this type of mitten in -10F and colder temps. My hand circulation doesn't work as well as it used to due to past frostbite (which is a result of stupidity on my part). The NO clothing is very good and very expensive. It works. I can endorse it because I've used it and it meets and exceeds their claims. But it is VERY expensive stuff.
BTW -- that furry patch on the back of the mitten? That's not for insulation. That's where you wipe snot off your face. No, I'm not kidding. For us guys with beards, it is OK to have rime ice. It ain't so suave to have snot running down one's face and freezing into one's beard.
Your best and first investment should be good quality long underwear. Women like silk for their unmentionable undies, so it follows that they'd like silk for their winter undies. Silk is an excellent insulator, it breathes well (ie, allows water vapor to escape), and it wears well. Look for washable silk, because you'd be using it often. If you don't want to pay up for silk, look for modern synthetics like capilene (from Patagonia) or other "breathable" synthetics. Or, go with merino wool, alpaca, etc.
Cotton and cotton blends absorb moisture and are not good choices for a base layer. If I am out hunting alone in cold temperatures, I will not wear any cotton on me anywhere. If someone ends up wet in cotton at sub-zero temps, it can be life-threatening. Wool is your friend. If you don't like wool, be ready to pay up for more expensive fabrics if you want to be out away from ready sources of heat or work afield. If you're someplace where, if you get wet, you can readily get inside, then cottons are OK. The first time you get wet in cotton in the deep cold, you'll see what I mean. Wet cotton is as good as no clothing at all.
Most heat lost on the human body is lost from your neck and head. If you keep your neck and head covered and insulated well, you're doing the single best thing you can do to avoid body-wide hypothermia.
5) This "public transit" question keeps popping up from people outside Wyoming. Outside of Casper and Cheyenne, we don't have much, if any, public transportation. The best assumption is that there is none.