I have biked in temperatures as low as 20 degrees (cold snaps, with no snow on the ground, are common in the Appalachian mountains of Pennsylvania). With cold snaps you rarely get any snow, the temperature is to cold to carry much moisture, but you can bike a fair distance. About half way through I tended to change t-shirts, they tended to get soaked with moisture and I felt better with a dry t-shirt instead of a warm but wet t-shirt (yes you can change in such temperatures, you just have to change quickly, your body can retain its heat for the 20-30 seconds it take you to take off the old and put on the new T-Shirt and put back all your other clothing.
For my feet I tend to wool socks and Army Combat Boots. About 10-15 years ago the Army finally switched to suede boots with Gore Tex Liners. With regular army wool socks it is sufficient (i.e. no need to actually winter boots, no snow and I am constantly moving so my body keeps me warm, you need winter boots only if it snows AND you have to wait around).
I use to wear long johns, but I then switched to over pants. The reason is simple, in most cold weather situations, you need to take off clothing if and when you get to hot, and put it back on when its gets to cold. It is much easier to take off a set of over pants then long johns. I use a farmer bib type over pants that are Gore Tex. In light rain or snow more then enough to keep me dry and warm. If to hot, I can un-zipper them not only in the front by along the legs. This permits me to use them even when it is raining but I am still to hot. I put them away in the Spring, really not usable above 50 degrees, but perfect below that temperature to about 10-15 then you have to loot into adding a set of long johns under your pants as your base before the over pants bid goes on.
I do a similar clothing mix when it comes to a Coat, Gore Tex over coat, over a Sweater or sweat shirt, over heavy shirt over a T-Shirt (And if to cold a set of long johns).
For my hat, under my Helmet I wear a Balaclava that extends to my neck. This gives me freedom of movement. I have also worn a thin baklava under the thicker balaclava for additional warmth. I have also wanted to go back to using Army Helmet Liners, I actually liked them for they are NOT knitted by woven material and thus better at wind protection. The down side is Knitted Material is warmer and can be switched over the head. The Army Helmet liner extends to under one's neck, but by using Velcro on its two extensions from the part of the Helmet Liner that goes over your head. The army extensions overlap and covers your neck using Velcro. Provides a very tight fit with woven material that is wind proof. Can fit over a knitted balaclava. I have been looking into getting a new one, but so far my balaclava have been sufficient, given I also tend to use a Russian Fur hat over the Balaclava in extreme cold weather.
As to my hands, I tend to have on me or on my bike at least four pairs of gloves. A light leather pair for temperatures from 50 to 35. I have a pair of Polyethylene glove inserts, to fit inside the leather gloves or any other cover for my hands. I have a pair of gore tex nylon insulated gloves for temperatures from 40-20. At these temperatures you have your greatest possibility of running into heavy snows. Below 25 degree I tend to switch to finger trigger Army Mittens. The mittens are NOT water proof, but it is rare to have rain below 25 degrees and almost as rare to have snow, thus you rarely need water proof material at temperatures below 25 (Even the Nature of the snow change, the heavy wet snow you get at about 30 degrees, becomes a light fluffy snow below 25, that tends to lay on insulated items instead of melting on them). I like the Finger trigger mittens for I can use the finger triggers to switch gears and then withdraw the finger into the rest of the mitten to keep it warm (This is the reason the finger trigger mitten was designed in the first place, you were NOT to keep your finger in the finger trigger part of the mitten, unless you needed it).
As to my bike, I tend to run slicks, unless you have ice or snow on the ground (and the snow has to be packed or covering ice, one can use slicks at very cold temperature, such as a cold snow on dry ground). On the other hand, ice and wet snow that turns to ice requires me to switch to studded tires. I have had a pair for almost 15 years. I tend to wait till it is clear the snow will stay on the ground for a while and the ice will NOT melt for a while (early snows that quickly melt are no grounds to change out of slicks). Late Snows that quickly melt, are grounds to switch back to slicks. Since I live in Western Pennsylvania we have winters when the early snows last till the late snows start i.e no snow that stays on the grounds for more then a few days. This is about half the winters and in such winters I never change tires.
On the other hands, in about half the winters, we have weeks of snow on the ground, with ice along with the snow. In such winters I have to switch to my studded tires. This last six weeks to two months (Early December to late February). Given that the studs have higher rolling resistance then slicks, I tend to avoid long trips with them, using mostly to go to and from work. The increase rolling resistance is clearly felt once you start to use the studded tires. On the other hand, you do NOT lose control of your bike when you go over ice or packed snow. The increase rolling resistance is why I tend to switch my tires late and switch them back early and why they have lasted 10 years. About half of those winters I never used them, in the the other half I did but for only two months and at a reduced biking level.
Cold temperatures should not be grounds to stop biking, but it also means one MUST be prepared to bike in such temperatures. Given that one often over heats in the winter for putting to much clothes on (For it is cold when you start to bike) and then freeze for lack of clothing (For you did not put on enough clothing and was warm till you came to a long decline when you do not have to peddle, but you end up with a lot of wind on you as you go down hill) one has to be prepared to switch what one is wearing. To do so you have to have the clothes on your bike (not necessary on you) and a place to put extra clothes you do not need right then and there. These two requirement can be meet with panniers. I do recommend a set of panniers to hold extra clothing that you may need, and the panniers supply a place to put excess clothes when you are over heated. I strongly recommend a set of panniers to hold such clothing. I tend to carry two around with me, for my extra clothing. I tend to also include an Army poncho and poncho liner.
The poncho and liner is a good emergency blanket if you ever need it (i.e. you need to hole up someplace till the weather improves). The Poncho is old fashion vinyl, so is NON-breathable but water proof. The liner fits inside the Poncho and provides some warmth, since it is polyester the warmth can be provided even if it is soaking wet. The poncho and liner is NOT the best tent, NOT the best water protection, Not the best sleeping bag, Not the best Stretcher, but is better then nothing if you need a tent, water protection, sleeping bag or stretcher. Thus it should be part of your emergency equipment on your bike (Along with a decent First Aid Kit). The Poncho and liner can fit in your panniers, if you have a set of panniers, thus I tend to like panniers on my bikes, especially if I am doing any winter biking.
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