It is possible to ride your bike through the winter. The right gear helps by Joe Clark OK, so it's winter.
Life goes on.
But bicycle clothing and accessory makers are quite happy to sell you specialized gear for winter riding, most of which is quite advanced and effective. Wear a helmet. Torso Wear an undershirt. Despite the lack of arm coverage, a sleeveless vest retains body heat nicely. Schlepping papers, clothes, a box lunch, and other gear can be a problem.