Buy a good folding bicycle that can be taken on the transit system you say is available. On days you don't feel up to riding both ways you can maybe do the ride one way. On days when the weather changes to really bad conditions after you've already arrived at work you can just fold the bicycle and ride transit.

Whichever bicycle you buy, be sure to check that studded tires will fit. Schwalbe Marathon Winter tires will fit inside most frames because they aren't knobby tires. I have some 20" studded Innova tires that won't fit inside the fork of my Dahon Smooth Hound. They did fit inside my recumbent bicycle frame with plenty of clearance.

I can't comment about respiratory infections. I got a cold almost a month ago and I'm still coughing due to too much mucus. One way to help lessen the amount of mucus is to take plenty of digestive enzymes. Apparently colds cause more mucus to be created and the bodies normal enzyme production can't keep up. When I take plenty of extra enzymes throughout the day my mucus level drops and I cough much less. This is a good tip for anybody who gets a cold or flu. I came up with this solution on my own. I've never read about anyone else doing it. It works for me.