I had a look at how the Spanish cavalry on the march to Tenochtitlan fought against the warriors of Tlaxcala. The Tlaxcala subsequently allied themselves to Cortez more out of fear of the Aztecs than of the Spanish.
The source used was Bernal Diaz who I find to be a very informative Conquistadore.
If it is of interest here is the link.
https://youdonotknowthenorth.blogspot.com