Have you ever seen snowfall when there is a clear sky? You may see light snow coming down but when you look up in the sky, you see no clouds or very few clouds. So how is this possible?
Some snowfalls are caused by elevated uplift. Elevated uplift is when air from the middle to upper levels of the atmosphere is lifted up. This occurs when there is a great difference in airspeeds from the surface to about 18,000 ft. The wind aloft is faster because there is less friction the further away you are from the surface. Because the winds are generally faster with height this can cause a twisting motion in the atmosphere. This leads to the atmosphere becoming unstable and allows air to rise, cool, and condense. This can lead to clouds and snow forming.
Snow falls at a very slow rate and because of this a cloud can form, produce snow, and quickly collapse or move away from where the snow was produced. The winds aloft are fast and carry the cloud downstream of the wind. So, by the time the snow reaches the ground, the cloud may be out of view or it may have dissipated.
Another cause for snow to fall on a clear sky is because the wind may have carried it to you. Snow is very light and the wind can move a snowflake horizontally a great distance. So it may be snowing a few miles away and the snow was blown to your location.