Good question, I personally wouldn't ride when it was that cold. I have never heard of a cold specific tire for a bike, that doesn't mean they do not exist. Motorcycle tires are softer by nature, that being said, softer compounds are more susceptible/affected by the cold. You would be the best safety gauge I guess.
That cold, now your talking ice patches, snow run off, sand, & at that point I say you are a braver warm blooded person than I. Good luck with your quest.