Of course, some varieties of camel did survive in South America and at least one, the llama, was domesticated as a pack animal and for its wool and meat.
One thing to consider about the horse is that it was one the last of the large ungulate mammals to be domesticated in the old world, suggesting that it was harder to domesticate, and that some prior knowledge and experience with animal husbandry might have been necessary before the horse was domesticated. Since there were no other large mammals domesticated in north america prehistorically, it is reasonable to speculate that north american natives lacking any prior experience with livestock would not have thought to, or been able to, domesticate purely wild descendents of pleistocene horses. At best they would be hunted and perhaps managed intelligently as a wild resource.
Following this logic, and considering the fact that the only area where large animals were domesticated in the Americas was the Andes, and presuming that horses also occur and survive in South America, I would suggest that the domestication of the horse would occur first in the Andes, in the context of a developing argricultural, urban, civilization. Horses would first be seen as meat and pack animals (it requires another conceptual leap to presume the wheeled vehicles would be introduced). Possibly, but not inevitably, people would learn to ride horses, creating faster communications and impacting military tactics and strategy, but that is really speculative.
Technological innovations require cross fertilization with equivalent developments elsewhere to acheive their greatest potential. Lacking such in the Andes, I suspect horses would remain little more than really big llamas in the economy and culture of Andean civilization.
What do you smart people think?