The lack of guns and horses was not particularly crucial to the defeat of the Americans.. or rather, the lack of the warhorse was not particularly crucial.
After all, a Spaniard could expect to get off one shot at a range between 50 yards and 100 yards depending on whether they were using a musket or an arquebus... without much accuracy and then have to reload again, which would take 30 seconds. A human running at average speed could definitely close the gap and kill their opponent in the time it would take to reload. And that's assuming they're running through an open field... if the natives managed to get a jump on the Spaniards... well... a musket can make for a good club.
And given how much the Aztecs out-numbered the Spaniards, even if they managed to get off more than one volley, it would've done them little good.
The real advantage to the gun during this time period is that they required less skill to operate than bows, arrows, atl-atls and javelins. All in all, a musketeer or arquebusier was far more expendable than an archer.
As for the horse, there have been relatively few times when heavy cavalry was really effective, and that had more to do with the fact that at that time, it was a lot harder for kingdoms to field larger armies... so they resorted to horsemen. Horse archers/gunpowder cavalry are much better, but they also have the disadvantage of being perched on top a 1100 pound target... Although, I will admit that shock cavalry could disperse the native's skirmishers fairly well assuming they survived long enough to actually hit their targets, but a lot of good it would do them in the Andes, the jungles of central America or the forests of Virginia.
As for the lack of iron... militarily-speaking, its not that important. The Spaniards reported that the Aztec's atl-atls could easily pierce their armor at the same range as their muskets. Their swords weren't able to parry like a European sword, but that's what they had shields for. And even the arrows of the North American natives was sufficient to pierce exposed flesh, and their clubs and axes could certainly do pretty well too. By the time something better would be needed, it would make sense in the scenario if they'd be able to trade for it... Play one European nation against another.
Imagine if the Aztecs survived long enough for the English to start selling them arms to combat the Spaniards...
Ultimately, the downfall of the Americans will be due to disease and economics. Focus on those two issues. The North American tribes couldn't replace their losses fast enough while the Europeans could... and that was because they lacked things like draft animals, iron tools (not weapons), had had certain cultural traits/traditions holding them back from rapidly adapting to more sophisticated forms of agriculture and industry.
So disease, as has been mentioned is important, and I would say is in fact, the most important thing. Disease alone killed far more than any armies could've. But after the initially shock of that, it should be a resistance to change and political unity that ought to be the source of doom for the Native Americans.
If the Aztecs or Inca manage to survive the initial Holocaust, however, they will be in a good position to adopt certain technologies, utilize captured animals and turn things around for themselves.
