Many snowfalls are the result of elevated uplift. Elevated uplift is the lifting of air in the middle and upper levels of the atmosphere (due to DPVA or jet streak DIV). The PBL is stable in an elevated uplift situation. Once snowflakes form, they have a significant distance to fall to reach the surface.
The terminal velocity of a raindrop is much greater than that of a snowflake. Therefore, a snowflake may reach the surface well after the cloud that produced it has past away. Also, wind can easily waft snowflakes a significant horizontal distance. This is especially true of small snowflakes that have a low density. When snow develops, the largest snowflakes will reach the surface first followed by the smaller flakes. It can often be observed that snow first begins heavy with large flakes then the flakes become smaller and smaller with time. This is especially true when the mechanisms that are producing the snowfall suddenly cease or move downwind.
Clouds that produce snowfall can dissipate rapidly and/or move downwind after producing snow. This can cause snow to be observed at the surface while the sky is partly cloudy or clear. The stars, moon or the sun can be out while light snow is still falling. Strong wind can blow snow well downwind from its source region. Snow falling from high elevations can be blown several kilometers from its origin point (middle and upper level wind is generally stronger than surface wind).