How did the Spanish effectively use cavalry against the Aztecs in thick Yucatan jungle?

Actually the times where he Spanish did try to use cavalry in rough terrain like jungles or urban cities, they had great difficulty in overcoming the Native armies of mesoamerica. Bernal Diaz del Castillo writes in his first hand account book, the conquest of New Spain of various engagements between the Spanish cavalry and the Natives where they fought in rough terrain (ambushed in the jungle or fighting in he narrrow alleys and causeways of Cholula and Tenochitlan) which tended to end poorly for the Spanish horsemen who were unable to make use of effective disciplined cavalry charges

The real times where the Spanish used cavalry with a devastating effect on the battlefield was on open fields where the mobility of cavalry could be wholly unrestricted and they could charge as a cohesive unit.

One battle in particular where this could be seen was the Battle of the PLAINS of Otumba, emphasis on the PLAINS part because it was this selection of terrain that allowed the pitiful squadron of Spanish heavy cavalry to prevail in slaying numerous Aztec field officers and ultimately cause the Aztecs to rout in confusion.

The only other times where the Spanish cavalry were effective against natives was during the early stages of contact between the Natives and the Spanish, as the Natives, wholly unknown to Cavalry shock warfare would often choose to flee rather than fight Spanish horsemen.