My nexus 8 has been fine for me down to -20C last year. Sure, it gets a bit stiff (pedals keep rotating when you remove your feet and are going forward) but I never had any real problems. It shifted all winter as well. Once or twice it shifted slow, so once I started pedaling it it'd SKIP to the right gear. So when it's cold I always soft pedal after I shift. (I stop pedaling WHILE I shift.)
I have had problems with derailleurs in winter. The first winter out here (which was a bit worse than the last two) I rode through a lot of snow on my winter bike. The cassette/freewheel got covered in snow, which then immediately froze. My commute is relatively flat, so I only shift between a few gears unless I'm stopping. Basically I couldn't shift to other gears because of the ice frozen under the cogs wouldn't let the chain sit on them correctly. Yes, my bike is kept in a garage out of the elements, but that didn't help.
However, I DO dread the day when I have to change a flat in the cold. But with that said, I've never gotten a flat with that bike and my winter tires on them. Honestly if it happened I'd probably just walk to the closest business and ask them if I could do it in there. It's Montana, they'd understand. It's dangerous to be out in -20C for long.
EDIT: It must be said that my IGH bike has full (and I'm talking FULL) fenders on it, while the derailleur bike had those little clip ons that just prevent your back from skunk striping.
EDIT2: Also of note. If you do have FULL fenders on a bike, be careful how low the front fender comes in the back of the wheel. Look at TSLs above. When the snow gets above the bottom of the fender, it makes it difficult to ride. Ask me how I know.
EDIT3: However, my BAD WEATHER winter bike (which is in reality just my spare mountain bike with nice nokian studded tires on it) is a derailleur equipped bike. I take this bike if the snow is REALLY high, or it's REALLY icy. It's not that the tires have more grip, I just have more control of a mountain bike than I do of my normally road oriented 700c bike. (Plus you can sit a bit lower and the suspension helps with ruts.) Yes the gears do get gunked with snow, but it's a tradeoff I'm willing to make for more control over the bike. Also the derailleur does drag in the snow if you're riding through enough snow.
Ask me how I know. haha