Shimano Sora shifter having trouble in the snow
I opened my shifter a bit, not disassembled the whole thing, but I was able to degrease it well. I then applied a lot of spray lube. I shifted up and down while spraying, making sure the lube got everywhere. I have used my bike every day in cold weather now, one day as cold as -10Celcius, everything seems to work. It can be a bit sticky, but I always manage to shift correctly now. I guess I'll have to apply lube quite often now, the spray isn't as heavy-duty as the original grease, but my gears work now.

Edit: I took my bike to the shop today, the shifter has gotten worse the last few weeks. When I picked it up they said Shimano has called back several models, a faulty spring seemed to be the problem. I got it replaced no-cost. My new shifter works perfectly in the -5C now!