Actually the issue of the horse being an "invasive species" is more complex then it first appears. Horses show up prolifically in the fossil record in North America and Cortez' escaped horses which became the first wild herds, it can be argued, were actually a reintroduction of the species. The first horses that the Native Americans tamed were from these herds that predate the American westward expansion.
They should be like other wildlife.
If they had a hunting season, they would be managed properly and not get to be over-populated.
The meat could be exported to France. It is eaten there all the time.
They are for the most part decended from escaped farm horses. Very few are from the Spanish Conquestidors.