The biggest change would be agricultural civilisation spreads south and east much earlier than OTL, so the region has millions more people come the 15th century. Horses would do very well in most of Brazil, so will greatly benefit the non-rainforest peoples there. Like OTL, they'd mostly farm maize and cassava. I suspect they'd domesticate the rhea and herd them around.
Actually, I wonder why the rhea was never domesticated by pre-industrial civilizations IOTL. Did their temperament and need for large spaces make it difficult for indigenous peoples to domesticate them, like the ostrich? Aside from that, llamas would definitely be valuable for their ability to traverse high altitudes and their wool, as there is proof they were independently domesticated twice IOTL.
The core of your civilisation would probably be in southern/southeastern Brazil, somewhat near the coast. Civilisation would expand across Paraguay and northern Argentina until it met the Andes.
Yeah, seeing as how civilizations tend to congregate around rivers with the examples of the Indus Valley and China, the Rio Plata likely becomes the central hub of some massive civilization, with a draft animal to produce more food. And with their control over Brazilian gold reserves located in Minas Gerais, I could see this becoming a very wealthy civilization very quickly. But without the natural barriers to defend itself, perhaps this civilization is constantly besieged and taken over by waves of nomadic invaders more focused on cavalry warfare from Patagonia similar to how the Mongols and Manchus conquered China.
The Amazon civilisations would certainly benefit from this as well and maybe adopt rheas, but I can't see horses being anything but a luxury there used for sacrifices or meat for important leaders. The Andean peoples will benefit more from it, since horses have the advantage over llamas besides tolerance to the cold and their wool, but I don't think they'll have TOO many horses.
Expanding on that, when horses do eventually get introduced north of the Amazon, they could end up thriving in the Llanos grasslands of Venezuela, which has a savannah climate and a strong culture of horseriding herders similar to the Gauchos of the Pampas. Maybe some kind of wealthy horseriding civilization emerges there and ends up introducing trade to North America via maritime trade, similar to how they were introduced across Southeast Asia IOTL.
That region would probably develop like Scandinavia--once their seafaring develops further, the Humboldt current would let them trade/raid places as distant as coastal Peru. In the east, Fuegians would settle the Falklands and South Georgia/South Sandwich Islands, but no further south because it would be too cold for farming or even grazing alpaca.
Now, here's a fun idea. If the Fuegans do end up developing a strong enough maritime culture by trading with the Rio Plata Civilization, I wonder if a few voyagers try to travel further north only to get swept astray by the South Atlantic Current. Eventually, after traveling across miles of ocean, they find themselves on the Cape of Good Hope similar to the Austronesians landing on the shores of Madagascar during the first millennium. While it's slightly implausible, as the journey would be rather difficult, it's still an interesting idea to consider.
But to me this seems like it wouldn't be until after 1000 AD or so, but in that timespan I'd expect to see a wealthier Mississippian civilisation (potentially one that's often raided by the Taino), wealthier eastern North America in general, and the emergence of pastoralism in Northern Mexico and the Plains, so the revolutionary bison hunting economy of OTL would be long established by the time Europeans ever see it.
I actually do wonder how European colonialism would be changed. By the time Colombus or Cabral discover the New World, much of South America is a civilization on the same level of development as something akin to Southeast Asia. Settler colonialism obviously doesn't occur on the level it did IOTL but maybe the process is more similar to India, with competing European trade ports and factories that eventually conquer sections of the continent after the industrial revolution. Now, here are some more ideas to consider.
Disease: An interesting idea I've thought about is animal-borne diseases such as hantavirus becoming a big problem for these civilizations, with hemorrhagic fevers occurring similar to how cocoliztli plagued Mesoamerica like a mix between Ebola and the Black Death. But while cocoliztli didn't spread to the Old World, perhaps these hypothetical fevers do, along with a mix of other diseases, changing the face of Europe forever.
Religion: Not entirely sure how this develops since there are a lot of fun ways this could go. Maybe shamanistic traditions of priests making deals with gods and ancestral spirits found among the Mapuche takes on a more legalistic form similar to OTL China as civilization develops. Maybe some sort of proselytizing religion or philosophy spread across the continent like Buddhism or Christianity. Since the PoD is so far back there's basically anything you can do with this.
Gender: I've recently read a book about the Proto-Indo-Europeans and it makes an interesting point that the reason why most Native American societies were matrilineal was because they didn’t have cows or horses preventing them from establishing societies centered around brothers and sons working together to protect their livestock. Apparently the spread of patriarchal societies correlated with the spread of pastoralism during the Bantu migrations in Africa as well. Idk where I'm going with this but it's still interesting.