Well, I'm no doctor, but I can tell you that since I haven't done my full commute on bike since the 2nd (one-quarter commutes on bike since then, except for today when I unintentionally slept in too late and had to drive), I feel measurably worse, have considerably less energy, and seem to need more sleep. So in my opinion, it's definitely better to ride, with the caveat that proper preparation (i.e., clothes) is taken.

In fact, I feel quite a bit worse even driving one day to work.

I can't wait for the next full commute. I'm considering changing winter tires to something that may be able to handle snow better than my Marathon Winters for this very reason. This heavy snow here is killing me. At least the last leg of my commute is relatively safe - the days are rare that I don't bike at least that, and yes, that 3.4 miles of riding for the day is worthwhile to me.