There’s a range of opinion of course, of course.
There’s a very small amount of scientifically dated remains of humans and animals from North American (and S A and the Caribbean for that matter) that antedate 1492.
Artifacts and petroglyphs related to horses have mostly not been scientifically dated (and thanks to NAGPRA etc, probably never will be), and oral traditions are, uh, fluid and not generally trustworthy, irrespective of their geographical and ethnic source.
Anyway, here’s one take on the “we had horses before Columbus” view:
https://ictnews.org/news/yes-world-there-were-horses-in-native-culture-before-the-settlers-came
Most of the "cactus hill" keyword:
Link to the paper: Early dispersal of domestic horses into the Great Plains and northern Rockies