Gordon has an excellent answer to one version of your Q. In case you are asking a more basic Q, here is a try at an answer.
Vini, think about the monsoons. Cooling the soggy parcel of air causes rain, but continued gradual cooling as it crosses an area of land does not necessarily create even heavier rain (leaving aside the rapid cooling that happens when it is pushed up a mountain). The parcel is dried out as it cools, so by the time it hits higher cooler land, it does not have that much precipitation to give.
Snow is just another type of precipitation. Like with rain, it occurs when somewhere in the air column the relative humidity humidity goes over 100% and the is at least some dust for nucleation. The history of the air matters. That very cold air in Norway had to travel there from somewhere warmer and more humid, perhaps even through Germany. As it traveled to Finland, it became colder and produced snow, drying it out, so by the time it got there it had very little water vapor to turn into snow.
In fact, we have a saying here where I am in Minnesota (USA) that it can be "too cold to snow". Our greatest snowfall is in March, early spring, when temps are right around freezing. It snow very very little in central Antarctica, the coldest part of the Earth.