I live in Canada, and we get a decent amount of snow in the year. However, it is very well known that you never get a lot of snow when the temperature is really cold. For instance, you never get a foot of snow (30 cm) when the temperature is at or below -30 °C (-22 °F).
What is the reason for this? Why doesn't it snow much when the temperature is very cold?
It's actually kind of the other way around, it's not that being too cold prevents snow from falling, it's that an absence of moisture in the air allows the atmosphere to cool.
Low pressure systems bring with them (relatively) warm moist air which precipitates as snow. The clouds overhead act as a blanket, and keep the surface air warmer. When the low pressure systems, clouds, and warm moist air move on, it creates the perfect conditions for the temperatures to drop. Sometimes the warm air systems are replaced by cold air systems when the winds change directions. Where I live the temperature changes drastically when the winds change, on Saturday it was -20°C when the wind was out of the North. A Chinook has blown in the past couple nights out of the West (air from the Pacific Ocean that's traveled over the mountains and warmed up because of adiabatic lapse rates) and now it's +12°C. That's more than 30 degrees in only a couple days.
Cold air holds less moisture than warm air, but it isn't so much the temperature that prevents it from snowing, the temperature of the air determines how much moisture the air can hold. Cold temperatures are an indicator that the air has no more moisture in it, ergo there aren't any weather systems overhead that can produce snow.
Any place that snows has the saying "too cold to snow," and it's generally true. Not that mere cold prevents snow formation, but that the coldest weather is generally clear and cold, with no precipitation. When it's a little warmer than that, and cloudy, is when you get more snow.
I've heard people say it's "too cold to snow" in England, when it's -5 °C. Super funny. In Ontario and the prairies, you'll get plenty of snow at -5 °C, but as you've noticed, not so much at -30 °C. Not because it's cold, but because it's clear - which also makes it cold.
Here is a link to a calculator you can play with: https://planetcalc.com/2167/
Let us say that it starts to snow when the relative humidity in the air gets over 100%. You will then see that there is far less moisture in the air -30 centigrade than at 0 centigrade. It is not that there is a sharp cut-off points when it stops to snow. It is just that the air above contains less and less water that can produce a snowfall, as the temperature decreases.
