I'd ask did they actually do any of it? I'm in the midst of academia doing a Ph.D. And doing that kind of stuff you tend to notice how many of the taken for granted assumptions we have about so many things, many of them “absolute truth”, are actually figments of popular culture's imagination.
For example, how many of us assume that medieval knights were slow, cumbersome and weighed down by all that armour, to the extent they needed to be hoisted onto their horses by a winch like contraption? And its all rubbish, that myth comes from an old film adaptation of Henry V (directed by Lawrence Olivier, I think). The point is, precisely, that the way we think people did things in the past, like how native Americans rode a horse, are probably much more conditioned by images we saw on moves that are not shaped by historical fact but by what people will find appealing to watch.
Id go ask some native Americans that still ride around on horses what they think; you might get a more historically accurate answer.