February is usually the month of crispy freeze. Luckily February is also the shortest month of the year. Fighting against cold is all about material science. Forget the two-striped sports socks. They are made of plastic, and simply useless in sub-zero temperature (and anywhere in public places). Forget cotton as well. You need to sweat just a little, and immediately cotton looses its ability to keep you warm.
Wool is good. If normal wool makes you itchy, try merino or angora. Prefer several thinner layers instead of one bulky sweater. Long Johns are good. Not very sexy but practical. Before investing into woolen Long Johns, check if it's ok to wash that particular piece of wool in the washing machine. Because if it's not meant to be washed in machine, but you do it anyway, you'll end up having felted, shrunk Long Johns... which will probably help you to sing like a soprano, but are awkward to wear. Wool does "autoclean" itself if you let the woolen clothes to recover in the fresh air after wearing them, but for the sake of the environment you will anyway need to wash your Long Johns every now and then. Felted Long Johns may not be the nicest possible clothes, but felted woolen mittens are great. They will keep both cold and wind away. And anyway, mittens are warmer than gloves with places for each finger separately.
In addition to lamb's wool there are other good material to keep you warm, such as silk, alpaca and some artificial fibers. And even though I was mocking the plastic socks in the beginning, it is ok to have small amounts of plastic in your socks - for example if you're planning to knits socks. Within sock yarn it's important to have some artificial fiber (e.g. 25 % acrylic) in addition to wool, to make for example the heels of the socks more durable. You don't want to have holes in the precious self-knit socks only after wearing them few times.