Horned Serpent (Water)
In Native American mythology, the horned serpent is mystical figure often associated with rain, thunder and lightning, and water. Unlike snakes as we associate them in the modern day or with their Slytherin mascot counterpart, in some folklore their scales were used for divination and their horns for healing. Since water is the element most closely aligned with compassion, love, healing, and psychism, this might be a house for the more empathic students — i.e., the Hufflepuffs.
The Wampus cat, in Cherokee mythology, is a "fearsome variation of a cougar". In East Tennessee, legend associates the Wampus cat as a spirit of death and earth, and J.K. Rowling mentioned in a Pottermore post that its hair is used in wand cores. As the element of earth is associated with prosperity, wealth, strength, and death, it may turn out that this is the house most akin to Slytherin, where ambition is prized most.
The Thunderbird (Air)
The thunderbird appears in a lot of Native American mythology, as a large bird with supernatural abilities of power and strength. While it has many different names in mythology, it is thought that its name originates from the beat of its wings causing thunder in the air. The element of air is most aligned with communication, travel, and intellect, so it might be safe to say that J.K. Rowling plans to have the Thunderbird house equivalent to Ravenclaw (especially seeing as their mascots are very similar).
Pukwudgies originate from Wampanoag folklore, and are said to be two to three feet tall and have features that resemble humans, except larger and more exaggerated. Among its many powers is the ability to create fire at will. Seeing as fire is associated with passion, desire, energy, and strength, this might be the Gryffindor equivalent in Ilvermorny.
Of course, this might all be nonsense, because there's no way to truly verify any of this before it hits Pottermore. That being said, it certainly seems to be in line with J.K. Rowling's plans for magic in North America (even if people have reservations about the cultural appropriation of Native American mythology). No word yet on when or if the quiz will go live, but I'm sure all will be revealed in time — or at the very least, hacked by a No-Maj with No-Patience.
Images: Giphy; Warner Bros