An interesting effort from NOAA as they share a process for mapping the approximate first day of snow
A quick look at the map reveals the obvious: the main factors that govern the average day of your first snow are the same main factors that govern your other major climate characteristics: latitude and altitude. In general, the farther north you are, and the farther up you are, the earlier the threat of first snow. In fact, the highest elevation stations along the spines of the Rockies have a year-round threat of snow. On the other end of the spectrum, the Deep South, Gulf Coast, Desert Southwest and Hawaii have many stations that get snow so infrequently, there’s no date listed (empty circles). In these places, there just aren’t enough events to make robust statistics.
There are also a few interesting, but more subtle, regional features. Across the Plains and Midwest, instead of a straight-up east-west pattern, there’s a slight northeastward tilt, where earlier dates plunge farther southward in the plains, relative to the more Midwestern states. It’s especially noticeable along a line stretching roughly from the Texas panhandle to Chicago. This has a little bit to do with elevation, but more to do with the fact that the coldest air associated with many winter storms—including early winter storms—often barrel down the high plains, corralled by the Rockies to the west.