At what temperature do you say its too cold to ride a bike?
Anything colder than -55F (-48C) is difficult to mechanically maintain.  Most lubrication products on the market for cold weather are rated to -60F (-51C).  Which means that at -50F (-45C) they become almost unrideable and at -55F (-48C) pretty much unrideable.

I am aware of products rated for colder than that, but they have issues that when stored at room temperature, they will turn liquid and drain out of whatever compartment they are attempting to lubricate.

Personally, I have several zones:

Anything above 70F (21C): too hot to ride comfortably

70F (21C) to -10F (-23C): perfect riding weather

-10F (-23C) to -30F (-34C): possible to ride comfortably with proper prep on appropriate bicycle

-30F (-34C) to -50F (-45C): not comfortable, but rideable (similar to 70F+/21C+)

below -50F (-45C): Not rideable mostly due to mechanical conditions

You may also check this quesion for answers regarding prep work for cold weather riding.