I find it hard to understand that the cultures of Middle and South America, being far more technologically advanced than those of the plains, disappeared within decades of Europeans arriving in their lands without ever attempting to use European weapons or horses, while the North American native cultures fought a retreating battle for centuries and adopted both firearms and horsemanship, the latter arguably to a degree that even exceeded that of the Europeans in skill and tactical importance.
There are a few reasons I can think of:
The geographical size of the plains vs the rather small mesoamerican land bridge might have bought the North American native cultures some time to adapt to European technology and culture that the cultures of the south did not have.
And/or the Spanish had a different approach to colonialization, in which the ruling class and dominant culture was replaced, but people's lives were never in themselves threatened by a population "replacement" as happened by the mass immigration and land occupation undertaken by the English (and later other European) settlers in North America. This can still be seen today in the demographical composition of these regions, where people of native descent make up a far greater portion of the population in Middle and South America, while they are a miniscule minority in North America. That way, the majority of natives in Latin America would never have had to contend directly with communities of European settlers, and thus would never be confronted with their weapons.
Are these explanations valid? Are there any others?
disappeared within decades of Europeans arriving in their lands without ever attempting to use European weapons or horses
This isn't quite right. It is correct that the Inca empire fell rather quickly compared to Western North America. But we must remember that this was much more of a coup d'etat than an outright conquest. The Spanish conquistadors came upon an Inca state in the midst of a war of succession, but a single Inca state all the same. They allied themselves with formerly independent groups and took advantage of the shaky political situation to overthrow a somewhat oppressive, rather homogenizing regime and replaced it with their own very oppressive, forcibly homogenizing regime. They were able to twist local traditions and methods of taxation for their own purposes, and the last Inca remnant in Willkapampa was defeated in 1572. The Aztec Empire suffered a similar fate, falling to the Spanish-Tlaxcalan alliance by 1521. A unified state facilitates a rapid conquest.
But elsewhere in Meso- and South America, this is certainly not the case. The Maya region has never experienced any significant degree of unity. Nojpeten, the last Maya capital, lasted until 1697, nearly 200 years after first contact. Groups in lowland Peru, Boliva, Ecuador, etc. were never really completely integrated into the imperial system. The most notable resistance in South America was that from the various Che (primarily Mapuche) peoples south of the Inca empire. The Mapuche successfully resisted Inca conquest for decades, before the Inca armies gave in and turned their attentions elsewhere. Not heeding Inca advice, the Spanish also tried to conquer them. They established a few settlements (Santiago, Puren, Arauco) in northern Chile, but were unable to reach southern Chile. Between 1550 and 1598, the Spanish and Mapuche frequently engaged in skirmishes, but never in a full-fledged war. Then on December 21st, 1598, the Mapuche general Pelantraru ambushed the governor of Chile, Martín García Óñez de Loyola, in his camp at Curalaba. Pelantraru's party killed the governor and all but two of his 350 soldiers and native allies. This inspired Paillamchu, the chief Mapuche general, or toqui, to initiate a large scale revolt against the neighboring Spanish settlements. This campaign was wildly successful. The Spanish settlements in Mapuche territory were eradicated- Puren, for instance, was captured and burned 5 times before the Spanish finally gave up. And to get to your original question... after years of fighting against the Spanish, the Mapuche very effectively adapted stolen firearms and artillery into their military. Under Paillamachu and other great strategists, they were able to outmaneuver and defeat Spanish cavalry regiments, even in the cavalry's "home stadium" of open field battles.
You're right that the horse didn't catch on in South America. This is true even today. This has more to do with the terrain than anything. Llamas and donkeys are simply better than horses at traversing the rugged Andean terrain.
And/or the Spanish had a different approach to colonialization
This plays an important part in the difference in the proliferation of firearms. In eastern North America, the British and the French (and to a lesser extent the Dutch and the Swedish) were vying over access to trade routes into the interior of the continent through the early period of their colonial efforts. While initially Native American communities had little interest in matchlock firearms, once flintlocks came on the market, they were particularly popular. So the French and British were actively selling firearms to their allies, as well as gifting firearms to help solidify those alliances. Meanwhile, the Spanish empire attempted to minimize the sale of firearms to indigenous peoples within and neighboring their territorial claims. Laws were passed restricting or outright prohibiting the sale of such weapons to Native buyers. Horse ownership was likewise restricted. In New Mexico, the Pueblo were allowed to work with horses owned by the Spanish colonists, but couldn't own them themselves. After the Pueblo Revolt in 1680 drove the Spanish out of the area, the Pueblo kept some horses for themselves but also sold huge numbers off to neighboring peoples on the Plains. There were already some horses owned by the Apache and the like, captured from the Spanish in raids, but the fallout from the Pueblo Revolt really kicks of the development of the Plains horse culture going into the 1700s. So throughout the 1700s, you have an influx of horses coming up from the Southwest and an influx of firearms coming out of the East Coast, mingling to varying degrees in the territory in between.