Uhh, what?
No. The cooler it is the better it should actually function, granted there's no humidity in the air.
A CPU having transistors and all that jibber jabber at it's most basic level manipulates resistance to calculate data. Resistance generates heat, which in turn actually generates more resistance. If the temperature is low enough it should really reduce resistance generated from the thermal aspect of it, therefore leaving more power in the system making it more efficient, and allowing even lesss power to be used in it.
A CPU doesn't have MECHANICAL functionality on it. It's logical via diodes and transistors and the likes. Since it has no mechanical functionality, putting it at below freezing temps wouldn't even do anything.
The only thing I can foresee is if it gets too low, it may lose resistance on the transistors and such, kind of like a superconductor having almost zero resistance but that operates at almost abslute zero. What I mean by too low is an unrealistic temperature not caused naturally on earth.
The only systems on your computer that would really be effected by "too cold" are mechanical devices that would potentially seize, and even then THAT'S only if there is MOISTURE that could freeze in the components, so anywhere in earths atmosphere. The only other "too cold" would be such a drastic difference in temperature that devices would go through the reverse of thermal expansion, and connections snap like saudering. That would require pretty much causing a cold snap like throwing raw liquid nitrogen on a board that was at standard room temp (70f)
Keep it above freezing and any day of the week you'll be peachy keen with SSD type hard drives. Those mechanical drives might cry a little bit but not really as long as they don't get below freezing while idling.