I only lived in South Dakota for one year. The first snow of the season was a blizzard in October that dumped 21 inches of snow.
It never got warm enough to melt it, and was followed by numerous snowstorms throughout the winter. Snow was piled so high it covered some of the windows. I went out one morning to get the mail, and sunk to my shoulders in the drifted snow.
That is unusual. The first full winter we were here, the first blizzard was Christmas, the next year we had snow in Oct, but it melted in a couple of days. It also depends on where you are in the state sometimes.