Wild horses are feral period.  I know many will argue with that because of the fact that the original horse did originate in North America, migrated to Asia during the last Ice Age about 10k years ago where Asians domesticated them.  Fast forward 10k years and reintroduce horses here...  Well they are half right, but the horses brought here 500 years ago are NOT the same horse that left 10k years ago.  Again Wild Horses are feral and herds must be managed by whatever means are necessary.