Is it ok that put computer box outdoor at low temperature.

Speaking of temperature, it can withstand such cold without any problems, as most electronic components can support up to -30 degrees or so before start failing (the same as over-temperature, they can also fail of under-temperature in extreme conditions like yours). It can even be used I guess in such conditions. But there is another real problem with outdoors and is humidity. Even a few drops of water that filter inside the box may wreak havoc in the circuitry of the motherboard and components, unless special protections are arranged for that. While temperature will not give you any problems, water and such can and is because of that that all computers are designed to run indoors.

i think it's not ok. in december in cool winter i had not used my computer whole 1 month and it was very cold temprature in my room where air comes from outside. when i started it after one month it did not start. then i opened my CPU and took the ram out and put it again in. and took wires out and put it again in. but after it did not start again i tried it next day but next day it started surprisingly. i told to my friend what happend with me. he said use it's because of cold . he said you must start/operate your computer in cold for some time in a week.

Well, to tell the truth, I, in Italy, especially in my city (Genova) Im certainly not accustomed to such low temperatures. I know from experience that a computer works best in a cold environment. But perhaps, in my view to get to -10 Celsius, it seems to me too, on the other side. I would not like it, you get damaged due to temperature is too rigid. I do not know who should be the optimal temperature regime. What I wrote, however, is only the fruit of my personal experience.