So now in the Harry Potter world we have an North American school of wizardry. Rowling's tale is an interesting one, and sets up for what is basically meant as a Bostonian version of Hogwarts. Unfortunately, the houses and their descriptions are vastly oversimplified, and there is no suite of seven books explaining various members of each house in depth to give us something to go by when deciding which House works well with each Harry Potter World fan.
The test is unhelpful, as it is with Hogwarts. The simplified notion of "Sneaky Slytherin", "Brave Gryffindor", "Smart Ravenclaw", and "Helpless Hufflepuff" sorted me into Gryffindor, when I must confess that only my aims could be possibly called Gryffindorian in that they are not evil. It took reading the books and thinking about the ramifications of each house to reluctantly conclude that I am Slytherin.
Unfortunately, there is no such material for the Ilvermorny houses. We appear to have "body, mind, spirit, and heart", wrapped around four descriptions of American Indian legends so surface and uninvolved as to be practically useless. The Pottermore site misplaced me, this time in Thunderbird, and I set out to develop my own understanding of what each house truly means.
Thunderbird
Simplified as "wizards of the spirit", Thunderbirds are said to be adventurers. It is no wonder that people think this correlates to Gryffindor. I would say, however, after reading up on the original mythical beast, that Thunderbirds are purpose-seekers. They are not 'adventurers' in the sense of enjoying trips out and back again with loot or knowledge, but 'wanderers' in the sense of flitting from place to place, seeking something that they will never find, and discovering many fine and useful things along the way, which may be discarded for others to more fully appreciate.
These folk are not setting out in bravery and determination to fulfill a specific quest. They are harkening to Thoreau's "Simplify", filling a backpack with all that they need, and setting out for a dream that they are not even sure exists.
Thunderbird attracts not only explorers/adventurers, but also idealists, dreamers, and wanderers. I would expect to find more Hufflepuffs and Ravenclaws here and fewer Gryffindors; very few Slytherins.
Horned Serpent
Of course, the relation to Slytherin and the snake is obvious, as is the relation to Ravenclaw in the simplistic description of the Horned Serpent as attracting "wizards of the mind". The old tales of this creature, however, show a rather different side to the wisdom-seeker. There is nothing particularly sneaky or prone to booklearning about the Horned Serpent. It is connected not only to written and remembered knowledge, but also to insight and divination. Headmaster Dumbledore seemed to place little interest or effort into teaching Divination at Hogwarts, but the Horned Serpent seems in American Indian folklore to place a very high value upon it.
Horned Serpent students are likely not so much interested in "knowledge" as in "truth", deep delvers, less concerned about the physical world, seeking the rare treasures. I would expect to find Ravenclaws in either Horned Serpent or Thunderbird depending on whether their search for knowledge is deep or wide. Horned Serpent no doubt attracts some Slytherins, but generally more for the search for power rather than cunning or manipulation. I would be more surprised to see Hufflepuffs or Gryffindors here.
Pukwudgie
Supposedly this house represents "the heart" and favors "healers". However, it was founded based, not on the actual Pukwudgie, but on the idealized stories of one particular member who acted rather contrary to type. The "historical" mythical pukwudgie isn't exactly Wizarding House Material. Still, we can work out a synthesis that gives us a good solid option for North American young wizards.
The Pukwudgie William decided for unknown reasons to devote himself fully to a particular young woman, the founder of the school, so naturally she would think to cast him in a softened light. This has resulted in a description of 'loyalty' and 'earthiness' that makes this seem like a lock for Hufflepuff. The beings themselves, however, are very unlike Hufflepuff. They are tricksters, dangerous, even evil at times, stealers of babies and livestock, not unlike the British creature known as the Brownie. They use cunning to provoke mischief, and are loyal only under unusual circumstances.
Hence I would see a Pukwudgie student to be openly anti-authoritarian, defiant, independent, willing to experiment and less interested in the kind of idealistic wisdom and morality of the Thunderbird or the Horned Serpent. I picture Pukwudgie House as performing the same service for Ilvermorny as the pranksters do for MIT when they turn the dome into R2D2 or disassemble cars and reassemble them inside offices. I would imagine that they learn by trying. It is likely that many Gryffindors can be found here, along with some Ravenclaws and a fair number of Slytherins.
If there are healers favored here, it is because they are better loved in a House where accidents are far more likely to occur.
Wampus
Supposedly this house "favors the body and warriors". That sounds very much like a lock for Gryffindor. Again, the lore apart from the world of Harry Potter suggests a very different kind of House. The Harry Potter lore suggests more of an exercise gym than a place of magic, a world of jocks and sword-wielding maniacs, looking to fight. The original mythical Wampus was a panther-cat creature into which a woman disguised herself in order to participate illicitly in a man's world. Some tales say that she listened in on the hunters and was locked into that shape as punishment; others say that she transformed in order to fight a terrible creature that threatened her family. As such, the better word would not be "body", but "real world" (as opposed to divination or spiritual journey) and the better word would be "hunter" rather than "warrior".
The hunter is secretive and sly, but noble and pragmatic. Wampus students would value cunning, trading of information, and seeking knowledge and insight insofar as it helps them reach their goals, rather than seeking either for its own sake. The Wampus is intuitive, rational, and careful, not apt to overplay its hand, not apt to bluff, and most dangerous when cornered or threatened. Warriors they might be, in the service of others, in the taking of territory and protection of their own rather than a drive for conquest or search for knowledge. Slytherins likely flock here, as do Gryffindors who secretly think that they might be Slytherin, plus a few stray Hufflepuffs that lean heavier on the "home base" than the "simple loyalty" aspect of their house.
Simple versions:
Thunderbird: House of wanderers, explorers, dreamers, idealists.
Horned Serpent: House of wisdom-seekers, divinators, and lovers of the esoteric.
Pukwudgie: House of the stubborn, the anti-authoritarians, the pranksters, the experimenters.
Wampus: House of the hunters, the goal-seekers, the protectors, the intuitives.
Based on this, I believe that the test result of "Thunderbird" was wrong, and I belong instead, if I belong anywhere in Ilvermorny, in Wampus.