I dont know about the Incas, but the Mexica putting gold on someone's mouth would've been... rude to say the least considering in nahuatl "gold" or "teokuitlatl" literally translates as something like "divine shit".

As for the claims about the spaniards being centaurs (a concept that doesnt really exist in Mesoamerican mythology) these seem to come from the same place as other myths about the conquest like the Mexica believing that the spaniards were gods or that they sacrificed "thousands of people in a single day", namely spaniard chronists writting after the fact and trying to shine the spaniards in a better light and the natives they just conquered as savages, a convenient excuse often used by colonizers of the time to justify their actions.

So far as I know there arent any records of the Mexica themselves (unless the spaniards had psychics with them, which I doubt) thinking the spaniards were some kind of animal-human hybrids, in their surviving records they often just refer to horses as "masatl" or "deer", for example this bit in Alvarado Tezozomoc's Mexicayotl, Chapter 109, - a Mexica noble recounting their first meeting with the spaniards (which allegedly he was there to witness or at the very least suposedely knew first account witnesses of)- notes of a report that was received by Moctezuma II:

Another day came Don Fernando Cortes to make landfall with a lot of other spaniards: they began unloading their horses and artillery in Chalchiuihcueehcan, that is today the city of Veracruz, but since it was Holy Friday...

There are also plenty of examples of native americans not being particularly disturbed by the spaniard horses themselves (rather by their tactical use) when fighting them, for example this early account in Cortez's own Second Relation Letter while on his way to Tlaxcala, and before he arrived in Tenochtilan he says:

and then they came together and began stabbing us and letting the others know we were in a valley, they fought with us in such a way that they killed 2 horses and injured another 3 and 2 on horseback

In fact many of Cortez's accounts make note of different tactics the Mexican and their allies developed to fight against horse ridders (though this one in particular is not about them), including the use of ropes, nets terrain, ambushes, etc... in none of those do the Mexican seem to give any particular supernatural property to the horses.

This seems to extend to most other peoples in America, the Pueblo inhabitants werent particularly awed with supernatural fear at horses when the Pueblo Revolt exploded, nor have I read anywere of them being particularly scared of them when they sold horses to other North American tribes following the success of the revolt and helping to give raise to the stereotypical mounted indian image.