"Yes. It has to be cold for it to snow, if your definition of cold is like that of most folks who live in the mid-latitudes. But the atmosphere must contain moisture to generate snow--and very cold air contains very little moisture. Once the air temperature at ground level drops below about -10 degrees Fahrenheit (-20 degrees Celsius), snowfall becomes unlikely in most places. Therefore, significant snowfall at such very low temperatures is rare."
For those craving a more technical explanation of the phenomenon, Fred W. Decker of the Oregon Climate Service at Oregon State University offers the following:
"The maximum concentration of (invisible) water vapor which can occur in air decreases to extremely low values at very cold temperatures. Most clouds form through a process called expansion cooling. First, a mass of air rises, causing it to expand (because of the lower atmospheric pressure). Expansion causes the air to grow cooler, which reduces the amount of water vapor it can contain. The 'excess' vapor condenses out into a cloud.
"At very cold temperatures, the expansion cooling process starts in air that already has a low water vapor content. Hence, the clouds that form at colder temperatures--if any form at all--contain much less suspended water in the form of ice crystals, the starting sites for snow crystal formation.
"At higher, but still subfreezing, temperatures, ice crystals hook onto each other to create snowflakes. In extreme cold, the ice crystals remain independent. There actually is no such thing as too low a temperature for some sort of ice crystal to form and for such crystals to settle out and land on the surface. Such a deposit of ice needles is not usually considered 'snow,' however; in the Arctic, for instance, we might refer instead to an ice fog."