Cycling on snow in extreme freezing conditions: will my bike break?
-20C is -4F, cold enough to be uncomfortable for humans, but not particularly cold for mechanical equipment.  You will notice that lubricants get stiffer, but generally they warm up rapidly when you ride and the stiffness will be gone in a minute or two.  Hydraulic fluids, et al, should be good to -35C or below, though they will stiffen before that, noticeably increasing the response time of the brakes.

Steel and aluminum do get more brittle at colder temps, but not to a noticeable degree above -50C or so.  Plastics and composites, on the other hand, are a bit more unpredictable -- most plastics get noticeably more brittle below about -25C, though no doubt there is a wide variation depending on the specific materials involved.

You will notice that the tires get stiffer, and people have reported difficulty with the tires becoming rock hard and spinning on the rims at low temps (eg, -20F).  Also, of course, rubber brake pads get harder, and rim brakes become much less effective.

There's really nothing in a bike that isn't in a car, and cars can handle -35 or -40C.  And the places where you have trouble with cars is mostly the battery and fuel system, components you don't have on a bike.