Have you ever tried to ride with a good set of studded bicycle tires? Spinning or breaking traction really is no problem as they grip every bit as good as a studded car tire (Directly related to tire pressure), but are subject to much less sideways loading due to significantly less speed and mass.
Regarding lights, you obviously need to get a light to see by, not just a marker. Such lights are readily available and not at all a speciality item any more. (more often the problem lies in the opposite end: That lights are too powerful without enough thought to the light distribution, but light solving these issues are also easily available)
Bikes are not unstable at low speeds. It is hard to balance with NO speed (But you can just put a foot down), as long as you have any speed at all stability is good. Braking power is as good as your traction, which is very good with good studded tires. Compared to cars bikes have comparable contact area in relation to mass (Pretty much given by tire pressure)
I ride safely throughout winter and here we have ice and snow for 4-5 months every year with temperatures as low as -25C