I've commuted on a bike in winter for 13 years now, but never as far as now, that is 30 km daily. I have a problem which I never experienced before.
In temperatures close to 0C and on paths covered with thin layer of melting snow turning into loose ice particles, the front wheel picks up these particles and splats them over the lower parts of the bike. Some of them get caught between sprockets, which they turn into an ice cone, causing the chain to lose grip and slip over them (with continues cracking sound, just like when riding with extremely worn out chain). This concerns fast gears (sprockets 11-17T), which I use most often.
There's no other choice then but to shift to lighter gears and make a helicopter out of the cranks, but that's annoying over a long distance.
I saw this question: How to prevent my hub body from freezing?, but the author does not mention snow at all, so I don't know if the same advice applies.