Basically since Native Americans don't have a lot of "monsters" people just kind of superimposed their own westernish ideas of what a Wendigo must be onto some rumors, kind of like they did with skinwalkers.
The first non-indigenous record of it is a kind of HP lovecraft unspeakable horror mystery monster you never see. Then some other folks like him wrote stories about the "wendigo" which I guess kind of sounds like "wind-igo" and is sort of associated with being cold, and they wrote about it being an air elemental and would smell or make shrieking wind noises. He basically said that Native Americans sacrificed human beings to it and cast devil summoning spells. (Which is some nonsense garbage and part of why natives hate being associated with witchcraft.) It's mostly non-described in there too, but gives the idea of a skull floating in the ether and it being a wind elemental.
Later, Stephen King put it into a book where he described it as having ram horns and later a movie, Pet Semetary, and he made this monster out of sticks and a deer skull. Which popularized that idea. But he just made it all up based on something else someone just kind of made up, with no basis in the original folklore.
And the yeti-like idea comes largely from it being a wind elemental with a big skull and using those as a jumping off point in comic books, which also spread to japan so they appear in a lot of videogames as a yeti-golem-thing.