Florentine Book XII - Nahua texts (Dibble and Anderson p19) - “All iron was their war array. In iron they clothed themselves. With iron they covered their heads. Iron were their swords. Iron were their crossbows. Iron were their shields. Iron were their lances.”
When the Spanish fled during the Night of Sorrow, those bodies who remained in the canals were looted “... were taken there as if merited the iron helmets, the iron corselets, the chain mail corselets, the leather shields, the iron shields, the wooden shields.” (Dibble & Anderson p30)
The eyewitness sources are inconsistent and non specific enough to be annoying, but no more than any ancient texts which we rely on as gamers anyway.
It is fairly clear from the Caribbean governor's letters home that the Crown just never supplied enough equipment to the colonies during this time period or later during the piracy age where the same problems continued. My assumption has been that the higher the status of the warrior the higher the likelihood they had access to armour from home which was sent out in smallish amounts. Those from the lower end made do with the cotton which was cheap and local. I sent Ged an extract from some of these letters which clearly show them receiving metal armour just prior to the conquest. In 1515 the Crown sent 200+ mail corselets and 50+ breast plate pairs (front and back) to the Caribbean colonies, I don't see any reason for them to magically disappear from use within 4 years. And that's only the paperwork I have access to.
Like Patrice I've done reenactment in breastplates in the Australian summer. You do what you need to do to survive balanced against comfort. Enclosed helmets really are the worst thing.