Why do electronics have a low temperature limit?
I can give you an answer because I had been one of those who either wrote or verified the specs of semiconductor ICs.
Legally and ethically speaking, I could only sign off on the parameters within which we have verified the IC/processor would work. And then my boss, and her/his boss, and everyone else would see the evidence of the tests, and they too would sign off on those constraints.
I could not ethically or legally sign off that a batch of processors would work at -100 C, if I had not put them thro the suite of tests at -100 C.
If you chose to use your equipment at -50 C, equipped with the processor I signed off on with a low threshold of -15 C, my company would no longer have any obligation to that processor. You have broken the warranty.
Testing at -50 C is a lot more expensive to do than testing at -15 C. I would have to verify the test site is actually -50 C--. It is also very dangerous.
Besides that, special/hermetic packaging is required for ICs to operate at extreme low temperatures. As an extreme example, plastic packaging could develop cracks or structural compromises when we pour liquid nitrogen onto them.
Differential expansion between the die and the packaging could tear the die away from its site of attachment, or crack the die.
There are stress tests that include simulating temperature variations in the functioning of the IC. Say your laptop is sitting in your car in frozen temperatures of -10 C. You turn it on and within 5 minutes it reaches a temperature of 85 C. And for the whole winter, you did that every evening. What about the head unit and the computer-controller that sits in your car, which you would drive for the next 15 years subjected to such fluctuations every winter in northern Maine?
There were too many mechanical issues that my mechanical engineering colleagues had to deal with when it comes to extreme low temperature testing. So, how low a temperature would you want us to verify and how much more extra are you as the consumer willing to pay for that low temperature testing?
We cannot just test one or two units to verify the absence of mechanical issues like incompatibilities between die and packaging, unlike people who hot rod their motherboards experimenting overclocking with the mere one or two processors they bought from ebay. We have to design the acceptable statistical distribution and the sampling plan that would fall into that distribution, that would apply to a stream of ICs flowing thro the product line.
Occasionally, the legality of the constraints could be rather involved, where the US govt agency requires the OEM to have their representative present while we test those ICs/processors, which could take a few days for a batch. That representative would sign off that we indeed had performed such tests at such constraints. That is how a $100 processor would cost the US govt $2000.
Such that if the US govt agency somehow decided to operate the equipment beyond the tested and verified constraints, we would no longer be legally held responsible for any mishaps or future malfunction.
I once designed an amplifier that would oscillate at -10°C. I fixed it by changing the design to add more phase margin. In this case, the oscillation did not cause any damage, but the circuit did not work well in this condition, and it caused errors. These errors went away at higher temperatures.
Some plastics crack when they freeze. Dry ice is -78.5°C, and I have broken a lot of plastic with dry ice. For example, I destroyed a perfectly good ice chest that cracked into little pieces in the spot where I had a chunk of dry ice in it.
In surface-mount designs, the differential temperature coefficient of expansion between the parts-soldered-to-the-circuit-board and the circuit board can cause large stresses. The stress-strain-temperature relationship often barely works over the specified temperature range. When the equipment is powered up, the hot components can change shape and break the brittle plastic, much like my old ice chest.
If the equipment is below 0°C and then you take it into a nice warm, humid office, water will condense on the circuit boards and can cause problems. Presumably a similar thing can happen with frost, depending on the weather. When the frost melts, there can be problems.
When I receive equipment in the morning that has been carried as air cargo, I assume that it has recently been very cold, and I let it sit around for some hours to warm up slowly and to stay dry before opening the box in the office.
Turning on very cold gear could be interesting. Some current-limiting components, such as a PTC or PPTC, will pass a lot more current.
The lubricants in motors such as fans and disk drives could also be a problem.
Other than maybe batteries and maybe the LCD components generally don't get damaged directly, even by extreme cold temperatures. If temperatures are changed to extremes, especially rapidly, there can be physical damage due to mismatched contraction with temperature or temperature gradients.
However, operation at cold temperatures may not be possible- components change with temperature, to the point where they may no longer operate reliably, may not start up or may quit entirely. The gain of bipolar transistors drops with temperature. Much below about 50K most bipolar parts stop working entirely because of carrier freeze-out. Electrolytic caps don't like temperatures much below freezing, and their changes (higher ESR and lower capacitance) can cause other parts to be damaged. Digital CMOS parts may function more-or-less okay, but the analog portions of a chip may go out of spec or fail to work (such as the clock oscillator or BOR or ADC in a micro).
Even more weird stuff happens as you approach absolute zero - at 4.2K (liquid helium), for example, a 1N4148 can make a relaxation oscillator. Get even colder and ordinary solder can lose all resistance, which sounds really great until you get trapped magnetic flux.