It can certainly get so cold that precipitation is highly unlikely, because the colder the air is, the less water vapor it can hold.
At temperatures around 40 degrees below zero Fahrenheit, it is very difficult to produce precipitation, and if it does snow, there is very little of it.
At very low temperatures there is essentially no moisture in the air, because most of the water that vaporized into the air at higher temperatures has already condensed or sublimated in the form of rain or snow.
When the temperatures rise closer to the freezing point, the water content of the air, and hence of any snow that precipitates, can be much higher.
If you look at precipitation records in Antarctica and the Arctic, when temperatures are very cold, there is little snowfall.
