As air cools, its ability to hold moisture decreases, making snow less likely. However, there is always some moisture in the air. Also, many times, very cold air is very stable (no rising motion, that in turns cools the air even more to squeeze the moisture out), so it is harder to snow.

Now, if it were possible to reach absolute zero (0 degrees Kelvin, which is equal to -459 degrees Fahrenheit), the answer would be yes. At that temperature, all water will condense out of the air, meaning it could not snow. Reaching absolute zero, however, is not possible.