Then what do YOU call it when people grow grains and other plants for themselves to eat? And they often grow those grains and other plants to sell to other people. I call that "farming" as well.
Do you think there is a fence around that area? If so, it was not the norm for most of human history. Fences take materials and labor to build.
So it would have been more normal for a person to spend their time herding the animals, or tether them, or just turn them loose to wander (depending on the time and the area.) The larger the human population in a given area, the more certain it was that the livestock were NOT wandering loose untended.
Also, a large number of large livestock used to be used for work: plowing fields, pulling carts, carrying packs, being ridden, and so forth. Those were certainly not being turned loose to find their own food during the workday. Also, their owners did not want them to wander away or get stolen. So they would typically be tethered, stabled, or fenced when not working (but often not a large enough fenced area to naturally produce the food they needed.)
Moreover, any area with cold snowy winters either had to do without livestock, or provide for their needs in winter. For example, there is a long tradition of barns, haymaking, storing grain and root vegetables, and similar activities in northern Europe. There is a similar tradition in the northern US and I think Canada, although of course that tradition was brought over by the Europeans. The people here before the Europeans had their own traditions, but livestock do not seem to have been a big part of them.
I'm glad it works on your land, in your climate, but that is not the pattern everywhere.
That style of raising livestock requires that people live in a climate with a warm enough winter, and you can't support very many cities with that farming model either.

Harsh?

There's a reason Europeans used words like "paradise" to describe the Americas when they discovered them. You've got workable temperatures, and enough rain that "succulent greenery" exists to be killed by your freezes.