> and winter encompassing traditional autumn and winter. The definition would be simple: summer is when it's kind of warm most of the time, winter is when it's kind of cold most of the time.

At least in the part of the US I'm from, we only used "Fall" for "Autumn", because colloquially it was already defined as a simple and pretty tight (but often slightly different each year) period: When the leaves on trees have changed color, but not yet all fallen off.