We cannot really measure a snowfall. When we say, “Four inches of snow fell,” what we really mean is, “Four inches of snow accumulated,” and that is something entirely different. We can measure a rainfall easily enough by capturing a sample in a rain gauge, but an accumulation of snow is affected by the amount of air trapped in the snow.
Humidity and temperature in the cloud can affect the size and shape of snow crystals as they form. If snow falls on a windy day, wind can break up the crystals in the air. All of this impacts the accumulation of snow on the ground. Broken crystals pack together densely, and a lower snow accumulation is the result. When conditions are cold and relatively windless, the snowflakes can be quite large and airy and break up very little on impact, resulting in a very fluffy snow which can accumulate readily. A typical snow accumulation is only 10-50% ice. The rest is air.
