I guess the CPU won't have problems going really low, like -50C or even deeper.
Most of the rest of the electronics in the system will in theory also have no problems with really deep temps, the drives (CD, HDD etc.) might be the first to run into problems due to the fact that their bearings might freeze sooner or later and even before that run under increasing resistance.
But you will run into other problems long before you would reach those temps. One word = condensation.
The cool air inside the case will start to condensate at around 56C (depending on humidity also lower or higher temp) and water is an arch enemy to electronics.
That's why people with water/pelt cooling have to insulate the CPU/Socket and surrounding area against condensation. That's also the reason why you don't see people running their setup in their freezer. Some cooled their whole mobo/cards in a freezer but their setup was in a mineral oil bath
Uhm, I'll better stop talking like I knew what I'm talking about and better go somewhere else, hehe
In general: the lower the temps below 55C, the more problems you'll encounter when you want to cool complete system. It's enough "fun" to deal with a water/pelt CPU only.
I'm trying to start a big debate on this, as I proposed a Full setup for The Fridge (freezer cooling) I'm particularly fearing the condensation issue, but I've got some tricks that may help. (see The Fridge connection or how...)
For the outdoor air thing, you don't need to worry, since cold outdoor air is USUALLY not below it's Dew Point (the temperature at which condensation occur for a given relative humidity). And as the air gets into the ducts to your case, it gets a little warmer, which is lowering it's relative humidity. Anyway, since in this case your computer is getting cooled by the cold air itself, there's no chance that any surface becomes colder than it (the air, I mean). (especially not your CPU). The condensation would occur outside the PC 's case, which you would take care to seal a little bit. One duct brings the air from outdoor in the case, the second duct brings it back outdoor...
Nice n' Easy
Cold air does not condense on warmer objects. Warmer air condenses on colder objects. If you pump enough cold air into your case to positively pressurize it, the warmer air in the room where you have the case will not infiltrate it and condense.