0 to -13? Wear any without fear.
I've never had any problems with my headphones when wearing them in winter. I often use my Senn CX300s or Beyer DT770s (these make great ear muffs!!), and sometimes the KSC75s during the winter. The temps here range from -20C to below -30C and I've never had any issues. When its snowing I only wear the CX300s, since they're the worst of the 3 and are the most protected from the elements when I have them on my head.
Edit: I agree with 12345142 about making sure the headphones aren't too fragile. The headphones I use are IEMs (CX300), or have a metal headband/clip which makes them quite sturdy. I would not recommend wearing something with only a plastic headband, although I see other people doing so daily around here. YMMV.