Very unlikely, (they are of Euro-Asian origin) - probably a biased producers take on things. Otherwise there would have been a similar animal (maybe not a horse - but similar) surviving pre-colombian.
The majority of opinion is the reverse - people/animals etc migrated from Asia into the America's. Until it was cut of.
The horse though does include zebra's and the ass (one of the ass's, being the producer of that program).