It's an individual decision that depends on you and your clothing. I've ridden in -20 F. I don't remember what the windchill factor was.

Some folks in The Great White North regularly ride in colder.

I'm sure there's a temp at which a traditionally equipped bike plain wouldn't function. I know that the pawls in freehubs/freewheels can freeze so that you just spin but I personally haven't had that happen.