When Narváez and de Soto arrived in northern Florida (1527 and 1539, respectively) they both had considerable trouble with the Apalachee, a densely populated Mississippian nation based near what is now Tallahassee, Florida (Tallahassee, "Old Fields" in Mvskoke, being named by the Seminole in reference to the extensive farmland that once surrounded the old Apalachee capital there). Narváez was run out of the region rather quickly and would die during the disastrous attempt to flee back to Mexico along with most of his men - only a handful survived after washing ashore in Texas, most famously Cabeza de Vaca, whose descriptions of the American Southeast would later tempt de Soto into his own failed attempt to conquer the area.

De Soto came with all the advantages he could muster: horses, firearms, crossbows, steel armor, and so on. Only the horses and steel plate armor really afforded him an advantage over the Apalachee however, and the Apalachee knew it and how to undermine that advantage. As de Soto and his men crossed a swamp, the Apalachee attacked. Here de Soto's horses could not charge, crossbows could not be reloaded and heavy plate armor was more a hindrance than a help. The Apalachee employed bows that are comparable to English longbows (similar estimated draw strength), were accurate at 200 paces, and could be fired 6-7 times faster than Spanish firearms, allowing the Apalachee to fire off a few shots and retreat out of range before the Spanish could retaliate (the Apalachee were described as running along logs on the water - narrow footbridges they had built so they wouldn't have to wade through the muck like the Spanish were doing). The Apalachee were capable of puncturing at least four layers of Spanish chainmail - after capturing an Apalachee archer, the Spanish wanted to test the limits of the weapon's abilities. After the archer penetrated through two chainmail hauberks, the Spanish decided not to waste anymore of their armor to find out if he could penetrate three hauberks at once, despite the archer demanding to be given another attempt since he didn't feel like he had done as well as he could have. Even when the arrows didn't punch through the chainmail, their arrowheads would shatter and the shrapnel would find its way through the links in the chainmail and do considerable damage.

The Spanish eventually got out of that swamp, and the Apalachee retreated once their enemy was on solid ground again to avoid facing off against their cavalry.

In order to defend against Apalachee archers, the Spanish employed the quilted cotton armor that had been developed in Mesoamerica, which was not only able to stop arrows, but was also more comfortable to wear in the subtropical climate of the Southeast than their heavy metal armor. The Spanish managed to capture the Apalachee capital of Anhaica and held it through the winter, but they had to endure a guerrilla campaign against them the entire time and by spring, de Soto decided to give up on holding Apalachee and sought other opportunities to the north and then to the west.

A few years later, when the survivors of the de Soto entrada fled down the Mississippi, they employed another local invention to defend themselves against the archers that harried them along the way. The Spanish added cane-shields to their hastily constructed boats. These shields protected against crossbow bolts and local arrows alike.

As a brief tangent, I'd also like to mention the rather unique qualities of Iroquoian arrows too, specifically their fletching. You're probably familiar with how most arrows are fletched, typically with three vanes placed straight along the shaft. An Iroquoian arrow had only two vanes, but these were twisted around the shaft. Essentially this is the archery equivalent of rifling; the arrow spins to stabilize its flight.