There are lots of resources on the web about cycling in winter, but since more often than not, people still (incorrectly) perceive near-zero temperatures as way too cold to cycle around town, here is my take on the subject.
I cycle year-round, roughly 10 to 30 km per day, in an urban environment in a continental European climate. Of the two main obstacles to comfortable cycling – rain and cold – in this article I will address the later: 3-4 months of daily sub-zero temperatures in the morning with minimums of -15 or -20 °C.
There are two keys to winter cycling: gear and best practices. With regard to gear, the objective is to prevent free air flow near the skin: a light windstopper helps keep you warm much better than a thick, but hard to zip up jacket, for example. Starting from the top, a good helmet is effectively mandatory. While specialised helmets do exist, they are rare and can be expensive. At the same time, a regular ski helmet with ear protection is probably available in most continental cities in Europe and not nearly as expensive. Compared to regular cycling helmets, ski helmets tend be much less airy and provide much better protection from the cold, especially when it comes to the ears and forehead.
As temperatures start to plummet, the streaming cold air can be quite harsh on the eyes: cycling glasses are therefore also mandatory. The lenses should prevent the wind from reaching the eyes to improve comfort as much as possible, but not cut off all air circulation because they would fog then. Completely transparent lenses are probably best as during winter precious little light is available anyway.
An ordinary scarf makes a big difference if you use a low-cut jacket or when temperatures go bellow zero. Using a thick jacket which can’t be properly closed so that air doesn’t stream under it is more or less useless: a scarf goes a long way to protect the neck, chest and (in extreme weather) the nose and mouth.
Winter cycling makes absolutely no sense without appropriate gloves: without them, the cold easily damages the skin and compromises safety because it impairs fist motor function, preventing safe breaking. Gloves should be effectively wind and water resistant and as long as possible so that they cover the wrist and that they overlap with jacket sleeves. A very nice selection and overview is available at BikeRadar.
Driving around town in winter, you frequently get in and out of buildings, exposing yourself to rapid temperature changes sometimes exceeding 30 °C. To be able to do this efficiently and relatively comfortably, a thick, easy to zip up jacket is mandatory. It should be wind-proof and at least mildly waterproof, although that depends on the microclimate you live in. There should be as little air flow as possible between your sleeves and gloves which is not always easy to do as wrists frequently flex during riding.
On really cold days, rain overpants can be used to introduce another layer to help protect legs against the cold. However, I find that until temperatures drop significantly below zero, it is not worth the trouble when I have no more than several kilometres to cover. That is about it, as far as cycling gear is concerned.
What remains are best practices, routines which make winter cycling a bit more pleasant. Chief among these is health. If a person has the flu, a high fever or a sore throat, cycling is probably not the best idea, especially in winter. Please use your common sense: some health issues have little to do with cold, but other can worsen in such conditions.
Health aside (assuming most people are generally healthy, most of the time), a very simple thing to do is to dress up a few minutes before you go out. In my experience, the body gets accustomed to low temperatures given enough time and internal heating released during normal cycling is enough to keep the rider comfortable. However, this takes time, so the first part of the trip is often the part when cold is felt most. Getting fully dressed a minute or two before leaving a heated room helps accumulate heat to help bridge the warm up period. When you reach wherever you are going to, you can do the opposite: take a minute or two to enjoy the extra warmth before you take your jacket off.
If you have an electric bicycle, you might do better using pedals until spring comes: riding with the motor generates much less body heat (as you aren’t pedalling or not pedalling hard) and at the same time, air flow increases and provides additional cooling – not a welcome effect. On the flip side, the ride is shorter when using the motor so the choice might depend on the circumstances.
One thing to definitely avoid is spending lots of time idle outside before a ride. Taking a walk around town with friends is a nice way to take in the characteristic pre-New Year atmosphere, take a breath of fresh air and stretch your legs, but after spending half an hour outside people get quite cold and cycling home after that in the same cold air could be seen as a form of self-induced corporal punishment.
The above list could obviously be improved by extension, but it is quite sufficient for relatively comfortable cycling down to -5 °C for typical city commutes and it makes cycling at temperatures as extreme as -20 °C manageable, if not very pleasant. From personal experience, night swimming on the Adriatic cost in the middle of summer is usually quite colder than cycling well prepared through city parks as the morning frost thaws and another day presents its opportunities…as short as days are during that part of the year.