saying about big snowflakes go away in a day, small snowflakes are here to stay?

Answer 1

My grandma says that in the winter. What it means is that the larger snowflakes come at the end of the snow or when the snow is tappering off.

The small flakes are what you see when the snow is starting or inprogress and these will stick because they are part of a small or large storm.

Answer 2

I can't find any reference to it's origin, these types of sayings often can't be credited. It's folk wisdom, big snowflakes mean they fell in warmer temperatures and will melt (hopefully) than powdery snow, which falls when it's cold.