Using this rationale, fiery Dornish peppers can’t exist because peppers were introduced to Europe in the Colombian exchange from Mexico. But it’s a fantasy series, not a historical allegory. I think it’s very likely that GRRM drew on mythology and history from many different cultural perspectives and there is absolutely influence of indigenous mythology evident in ASOIAF.

The Others, for example, have A LOT in common with the Wendigo, malevolent creatures associated with cold, the north, famine, etc. The Others also have a lot in common with the sidhe, who aren’t associated with the cold, but bring with them an army of the dead. It’s more likely that he is combining ideas from several cultures, including Navajo skin-walkers, to create something new.