Studying our atmosphere is of highest importance, since data about our atmosphere can let us predict events or simply temperature on a specific day. If you fly with a plane, you will observe little ice crystals forming around the frame of your window. It is definitely nothing to worry about, as it is all simple physics and natural.
In this case it is similar to your ice drink sitting on the kitchen table. The warmer side of the glass (in this case the outside) decreases in temperature, due to the cold liquid inside the glass. This means it transfers coolness to the surrounding air. That surrounding air cools enough to cause the moisture it contained to condense into liquid that you will see sticking to your glass. However, if the glass was cold enough, it would freeze that condensed substance. That tells us, that the window of the aircraft is that cold, that the condensation freezes. 
(Hole in an airplanes window with ice formed on the edges)
But why is the window so cold ? Isn’t it still inside the atmosphere ? Well, the cruising altitude of a plane is around 12 km. That means, that the plane is located inside the troposphere. As height increases, the temperature decreases by –10 degrees Celsius. That means at that heights, temperatures fall to almost –60 degrees Celsius. To understand why the temperature decreases with height in the troposphere we will have to have a look at the Meteorology of the troposphere. The troposphere gases, which consist of nitrogen (78%) and oxygen (21%), with the remaining 1- percent consisting of argon, (0.9 percent) and traces of hydrogen ozone (a form of oxygen), and others, absorb very little of the incoming solar radiation. The earths absorb this radiation instead. The troposphere then absorbs heat by the conduction and convection process, because the earth releases heat. Evidently, this heating process is the most effective near the ground, thus the temperature gradually decreases with an increasing altitude until the tropopause (where the troposphere ends and the stratosphere begins) is reached. Mountain climbers have to wear thicker and more isolated clothing, because as they start to climb, they will increase in altitude and at some point the temperature will change accordingly.
(Pyramid representing the temperature increase per km with colors)
Güney 9BL2

