I'm sure we all clearly remember the scene in Twilight when Bella is beginning to get suspicious that there's something "special" about Edward and goes home to furiously type things into Google. The camera views of what she pulls up are succinct, yet clear enough to give us the understanding that Bella has come across some Quielette legends stating something about "The Cold One" and how this cold one is a vampire. But,what is The Cold One? Is there actually a vampire known as this?
Well, the closest thing to any vampire legend that would bear any similarity to the legend of The Cold One would be the Apotamkin. This creature is unlike most other vampire folklore because it's exclusive to the Native American people. The Apotamkin was a bona fide vampire however, with all the abilities and super strengths of other vampires that we know. It was believed among Native Americans that the Apotamkin would feast on the blood of any animal or human. And it got its name just the way you would expect - Apotamkins were very cold to the touch, mostly because they were dead bodies.
However, it's been said that the Native American never really believed in the Apotamkin and that it was a cautionary tale told to children. This was used especially when warning children about wandering off by themselves with no supervision.
And, as for Twilight, Stephenie Meyer has said that in regards to her version and her version alone, she had no similarities in mind when writing the book. She simply needed to create random bits of Edward's character and piece them together, cryptically, with mythical vampire folklore. Clever, though, how perhaps even without knowing it, Meyer has combined her own imagination of the Quileutte legend, with actual Native American vampire folklore!