I suspect that the haying was not reason for the harvest celebration. It's not uncommon to get more than one cutting per season and the name came more from the coincidence of the last cutting falling around the same period. Once you have the winter's supply of hay in and the pastures are getting poor, it's common to graze the hay fields. Besides... food for folks is a higher concern and reason for celebration... by people, that is. The livestock would vote differently if they could. LOL

Pastoralists, hunter gatherers and farmers all live closer to nature and the seasons. It's urban folks who end up truely out of touch...

more so today, because fewer and fewer folks have "country cousins".