Knever

Corrected entry: When the DeLorean suddenly appeared in 1885, the Indians have absolutely no reaction at all. There is no possible way that they wouldn't have been the least bit spooked or confused, and we should have seen some semblance of this in their actions, but they just keep charging on like nothing happened. It'd be like a an alien spaceship appearing out of nowhere in Times Square and people not even batting an eyelash.

Knever

Correction: Even putting aside that not reacting the way you expect is not a mistake, they were more focused on being chased by the cavalry, and they may well have assumed the Delorean was another "white man" invention like the locomotive.

Would it not be a bit mysterious if the Americans had invented the car but still ride horses?

The Indians did not know that it was a car or what its purpose was. All they saw was a strange device obviously invented by the "white man."