the area where a horse lives A small, usually enclosed field near a barn or stable for pasturing or exercising animals.

The ways to retain the fertility of the soil are crop rotation, animal pasturing (which can be considered fertilizing) and fertilizing either with natural or artificial fertilizers.

Haying, harvesting crops, spraying fields, seeding, tilling fields, breeding cows, vaccinating calves, pasturing livestock, feeding livestock, etc.

i would expect people to do lots of farming

Yes, you can. However because there is increased risk with surgeries in horses, the cost of surgery for horses is quite high and because breeding can typically be prevented by simply pasturing stallions and mares together it isn't done terribly often.