I'm on a Xtracycle with 700c wheels running Schwalbe Marathon Winters when it's icy. The safest way to ride on snow is to avoid the shoulder where refrozen slush resides. I typically end up on the white line because this is normally cleared off by traffic. Check the Winter Riding discussion for more tips.
Respiratory: cold air will shrink mucous, so it might be a temporary relief; reduction of dairy in the diet often lowers mucous as well. Caffeine helps shrink mucous, too. The best thing is lots of sleep and a good diet (here's a
summary of some tips I just found for avoiding colds, I follow similar philosophy).
If you don't have a trailer, you might consider one, even for going to work.