The scientific principle is Boyle's Law. It basically says temperature and pressure are related, lower pressure = colder and higher pressure = hotter. The air in the atmosphere is a higher pressure than the air in the intake (of course, engine vacuum), so its temperature drops with a decrease in pressure.
On Dodge K-cars, there was a water-heated space in the intake manifold to prevent the same issues from cropping up. Two small hoses connected the intake manifold heater plate to the coolant system, which helped keep the area frost-free.
The opposite effect is seen with the output tube on an air compressor, those get very hot due to increase in air temperature with the compression. This is why intercoolers are installed on some turbocharged engines, gets rid of some of that additional heat.
Airplane pilots have to watch out for the same problem, there are particular combinations of ambient temperature and humidity which can lead to the carburetor throat icing up. Usually it's when the dewpoint is within five degrees of the temperature.
If the engine RPM is high enough, the ice crystals can be drawn past the carb. throat before they get a chance to cling to the sides and cause trouble. If the system is running fine despite the frost on the outside, I wouldn't worry about it too much. I'd restore the mixture settings to original (or otherwise tune it for just-right), so you don't damage the engine. Since gensets always run at a constant high RPM, it should be fine, especially with Recovry4x4's note of personal experience.
