Reddit reviews The Horse in the City: Living Machines in the Nineteenth Century (Animals, History, Culture)

Well, unfortunately I don't have a good reference for rural horses (which I think you're most interested in) but I do have the book The Horse in the City which has a whole chapter on feeding horses during the 1800s. While it focuses mostly on urban areas, it does say that farm machinery for baling hay first appeared in the mid 1830s. The other primary thing fed to horses was oats.

Hay was often shipped in to cities across state lines and even internationally. At its peak nearly 15% of all farmland in the US was devoted to hay, and standards for shipping hay first appeared in 1877.

I'm just speculating from here, but based on the book I would imagine that horses did eat hay in the Old West. In the early 1900s California was one of the top 10 hay growing states and the rest were all in the midwest (well, other than New York). Anywhere there was a railroad hay could be shipped in, and anywhere crops could be grown hay would be among them. The demand for hay in cities drove a pretty rapid evolution in baling and shipping efficiency, and no doubt rural areas benefited from it as well.

Those are great questions! I went looking to find the answers for myself and found this website that explains it all.

It also reminded me that I want to read The Horse in the City: Living Machines in the Nineteenth Century. Before the advent of automobiles & trucks, horses were indispensable as a source of power and transportation in cities everywhere. Cities had to deal with housing, care, manure removal, etc.

But I'm going to get it from the library and read it.