One phrase that is heard from time to time is that, "it is too cold to snow today". In actuality, earth's troposphere is not too cold to snow but rather it is "too dynamically stable to snow". Dynamic stability may be present due to low-level cold air advection, a lack of upper level divergence, and/or a lack of low level convergence. Also, if dynamic lifting does occur it may not produce precipitation that reaches the surface due to low relative humidity values in the lower troposphere.
The ingredients for snow are: (1) a temperature profile that allows snow to reach the surface, (2) saturated air, and (3) enough lifting of that saturated air to allow snow to develop aloft and fall to reach the surface. In a situation when it is said "it is too cold to snow" there is in reality not enough lifting of air that causes snow to reach the surface.
The phrase "it is too cold to snow today" probably originated as a misapplication of the relationship between temperature and the maximum amount of water vapor that can be in the air. When temperature decreases, the maximum capacity of water vapor that can be in the air decreases. Therefore, the colder it gets the less water vapor there will be in the air.
Even at very cold surface temperatures significant snowfall can occur because: (1) intense lifting can produce significant precipitation even at a very low temperature, (2) the temperature aloft can be much warmer than the temperature at the surface. The relatively warmer air aloft can have a larger moisture content than air in the PBL, (3) Moisture advection can continue to bring a renewed supply of moisture into a region where lifting is occurring, (4) Even at very cold temperatures the air always has a capacity to have some water vapor.
If the air cools to truly frigid Arctic temperatures such as -40 C and below then the moisture capacity of the air will be so low that likely not much snow can occur. Only at these extremely low temperatures is the phrase "it is too cold to snow" fairly valid.
At the temperature of absolute zero ( 0 K, -273 C, -459 F) all air including water vapor condenses and loses all molecular energy. The temperature can not cool below absolute zero.
