im interested in learning this since cortes' victory over an aztec army who literally outnumbered his tired force by thousands of men, was primarily attributed to his use of shock cavalry and the aztec's lack of experience with the shock cavalry tactics.
I'm not an expert in the battles prior to the colonization of Latin America, but this is the first time I hear about shock cavalry used against the Aztecs.
The Course of the Mexican History, 7th Edition by Michael Meyer, William Sherman, and Susan Deeds cites that Cortes brought sixteen horses and an unknown (or unstated) cannons. Cortes lost horses to several skirmishes during his journey. For example, Meyer writes that Cortes lost two horses in a skirmish with the Tlaxcalans, which limited his ability to use shock cavalry tactics.
It's hard to tell an exact number due to the fact that numbers change between sources and events that ocurred. For example, before beating Panfilo de Narvaez, Cortes counted with at least 500 soldiers (16 of these mounted). These soldiers were not all professionals. Some were sailors, which I assume received some combat training, and irregulars picked up at Cuba. After beating Narvaez, he added at least 80 horses to his army along with the survivors of Narvaez expedition. Prior to the riots at Tenochtitlan and "La Noche Triste", Cortes enters Tenochtitlan with at least a hundred men in horseback.
Though I don't doubt shock cavalry tactics won Otumba, I don't think it was the sole factor. Sadly, Meyer doesn't go into detail choosing to focus on the siege of Tenochtitlan. However, Cortes traveled with war-dogs, bronze cannons, and other weapons. I can infer from numbers given by Meyers during the siege of Tenochtitlan, Cortes had 16 bronze cannons available. I wouldn't be implausible for Cortes to have access to some cannons during Otumba. But that's just me rambling about...
To directly answer your question: no more than 100 mounted soldiers and no fewer than 86 (a number reported during the siege of Tenochtitlan).
Per Gomara, Cortés' secretary who wrote his biography several decades after the fact, Cortés headed back to Mexico from the coast with 100 horsemen. He does not discuss how many Spanish, Tlaxcalans, or horses died in the fighting before La Noche Triste, but does say that on that particular night:
450 Spaniards died, 4000 Indian friends, 46 horses, and, I believe, all the [Aztec] prisoners.
Of course, Cortés, in his 2nd Letter says that he returned to Tenochtitlan:
at the head of 70 horse, 500 hundred foot, and a fair number of guns.
Later on he mentions that he was also accompanied by more than 3000 Tlaxcalans.
Cortés states the casualties of La Noche Triste were 150 Spanish, 45 horses, and more than 2000 Tlaxcalans. This only lists those who perished on that particular escape attempt, which proved successful, if costly. By his own account, he had 24 horses when he reached Tlacopan.
On the flight from Tlacopan around the lake shore, various battles mean that several more horses were injured and at least one more killed prior to Otumba/Otompan. This is consistent with Díaz del Castillo who reports 23 horses following La Noche Triste.
Gomara's exaggerations are part and parcel of his writing, which is basically a hagiography of Cortés. Gomara himself was not in Mexico, and never traveled to Mexico, instead collecting all of his information from Cortés several decades and chips on the shoulder after the fact. Díaz del Castillo's "True History" was written partially as a rebuttal to Gomara and on several occasions calls out Cortés' secretary for inflating numbers on both sides.
I previously wrote a bit more about the battle, if you are interested.