Others have provided really good answers for why the Spanish themselves were not really that much more impressive than the native fighters in mesoamerica. But I do want to bring up that there is another angle to this, which is that the conquest expeditions of the Spanish would essentially always make a point of attempting to gather native allies to fight with them, or in later expeditions bring along native allies from previous successful expeditions. Native auxiliaries vastly outnumbered the actual members of the Spanish expeditions in most cases. In his account of the conquest Bernal Dias essentially admits that if the Tlaxcallans had maintained their hostile attitude to the conquistadors after a series of battles the conquistadors narrowly won, the expedition would have basically been doomed. Their role was so central that to many indigenous mesoameircans, the exact nature of what the conquest was took a very long time to sink in for them. Several early native narratives of the conquest treat it less as a totally foreign conquest and more as an episode in the rivalry between the tlaxcallans and the Aztecs, with the Spanish being simply the tlaxcallans tool in destroying the Aztec empire. This trend continued with the expeditions into the Yucatan, where Mayan accounts also heavily emphasized the Nahua allies of the Spanish in securing victory. It was largely the conquistadors themselves who tried to present it like they did it all by themselves, and that was basically all a venture in self aggrandizement to secure promotions and rewards from the Spanish king.

This also meant that from a military perspective, the Spanish soldiers are better looked at as a unit within a larger native army than as a force on their own. Which impacted their strategic and tactical role in important ways, and tends to mean their relatively small advantages were accentuated greatly. Being a part of a larger force meant that the Spanish could deploy where their armor, weapons, and horses would create the biggest impact and cause the most panic in the ranks of their opponent. The conflict between Cortes and the tlaxcallans early on especially illustrates this, where on their own the conquistadors are bogged down fighting large numbers of enemies and reliant on shock tactics to pull off a narrow victory, but as part of a larger coalition are in fact able to pull off stunning victories against the Aztecs.

Edit: forgot to mention my primary source for this is Seven Myths of the Spanish conquest.

The disparity of "metal weaponry, guns, and horses" is less than you might suppose, given that the Spanish were a tiny minority in the major campaign against Tenochtitilan, with mounted troops an even smaller minority. Gunpowder in many major clashes was limited or even non-existent, with the Spanish going so far as to commision crossbow bolts from Indigenous groups and even trying to build a trebuchet (which failed ignominiously).

The Spanish, from their very start, allied with Indigenous peoples who consistently made up the majority of the forces in any particular battle. The key example of when the Spanish attempted to go alone into enemy territory is when Cortés led a group from Veracruz inland across Tlaxcalan territory to the Aztecs. This was a disastrous outing which very quickly devolved into the Spanish pushed back into a defensive retreat which was only alleviated by the Tlaxcalans relenting and extending an offer of alliance, instead of annihilation.

Furthermore, there is no evidence that the Aztecs were "in decline," at the time the Spanish arrived, but were instead at the height of the power. There was, however, infighting which was exploited by the Spanish. In 1515, there was a succession dispute over the Acolhua kingdom, which led to its bifurcation between a more Mexica-aligned (even puppet state) southern portion and a more independent northern area.

The ruler of the northern half, Ixtlilxochitl, would ally with Spanish after their expulsion from Tenochtitlan, and would eventually lead to their allied forces seizing the whole of the eastern shore of Lake Texcoco. This is an underappreciated strategic victory which granted a lacustrine base of operations against the Mexica. This had less to do with Spanish might of arms and more to do with Ixtlilxochitl taking advantage of a chaotic situation. (See my comment on the Battle of Otompan for more info and for an actual example of how Spanish cavalry made a difference tactically.)

The reality is the Spanish represented a form of heavy infantry and gained early advantages from cavalry and artillery, but those advantages were blunted by their small number in proportion to the Tlaxcalan and Acolhua troops who formed the majority of the fighting force, not to mention the problems with gunpowder supply. Many of the advantages of the Spanish were blunted by adaptations by the Mexica to defend against the new weaponry and tactics they were facing. What is lost in the discussion of the "Conquest of Mexico" is that, in the end, it was largely an assault on a single powerful city, and even that took eight months of hard fought, grinding warfare across multiple fronts.

For more information, please see my previous comments:

• How effective was Native American weaponry and armor when compared to contemporary european equipment in 1500?

• Did the Aztecs,Incas or Maya ever try to adapt European technology before being defeated?

There's always room for discussion, but perhaps the section on Pre-Modern Non-Western Warfare from our FAQ will answer your question.