Never heard of a cooperative specifically for hay harvesting, cooperatives are usually more broadly-based than that, but that doesn't mean there aren't any. Here in Saskatchewan, for instance, The Co-op, as everybody calls it, is an integrated big business in both wholesale and retail, runs gas stations, farm supply shops, dry goods stores, grocery stores, lumber yards, hardware stores, home improvement centres, the works, all over the province.
Usually, if a landowner has a hay crop but lacks the means to harvest it, the crop will be sold standing in the field, and whoever buys it has to arrange for baling and collection. It's not likely to be six feet tall either, maybe half that. My father-in-law used to grow 160 acres of alfalfa every second or third year, rotating it around various fields--alfalfa's a nitrogen fixer, if I remember right, helps recover soil fertility from depletion by cereal crops--but he had no animals to feed it to or the equipment to cut and bale it, so he'd just put an ad in the local paper to sell it standing. It was sold on a per bale basis, so the buyer would do the baling, then we'd go out and count the bales, and of course the guy who did the baling always said there were fewer bales than we counted, but that's another issue.