Ah, so those horses are semi-feral then. Technically owned, occasionally rounded-up, but left to fend for themselves otherwise. Barely a hundred years ago great swaths of America raised horses that way. The dubious "legacy" of that time period is the mustang.Here people do make some money because most horses are just living their life in the mountains (they don't spend money on them) and every year or 2, the owner goes trail riding and get the horses down the mountain, catch the young ones and train them to be ridden and then sold.
Many places still breed horses that way. Including some places you wouldn't expect, like Great Britain. The Dartmoor, Exmoor, Fell, New Forest and Welsh Ponies all have semi-feral populations there.
Germany, France and Spain also have notable semi-feral populations of specific breeds.