Not only did I not ask that, I don't believe that the equinox is traditionally known as the beginning of autumn. Traditional terminology always marks the solstices and equinoxes as the middle of the season in which they occur, because that is obviously the way seasons work. Compare Western European "Midsummer" [the solstice] or Chinese 立秋 ["beginning of Fall", August 8; compare to the equinox on September 23, or to the "Mid-Autumn Festival" 中秋节, fixed to the full moon, but generally around late September].
The equinoxes and the solstices are marked on modern calendars as the beginning of their respective seasons, but I have never heard anyone attempt to justify that. I tend to assume it's the result of the calendar-buying population not having any reason to care what season it currently is.
But even among modern calendar-buying people, I believe they think of big snowdrifts as something that happens in winter, not something that happens in late fall and continues through winter. And the calendar doesn't agree with that.