That's an inaccurate generalization on the same level as calling all Indians dirty savages. The ancient Romans were into bathing, and the Europeans all through history indulged in hot baths more often than is generally known. Many villages had bath houses--the Nordic people had their saunas. I don't think your average Native American bathed any more often in winter than your average European.
You're right about the generalization... but on 'average' the eastern and southeastern North American Indian did bathe more often, typically daily, and even in winter, and what is more, never peed in a stream or body of water, something which rather shocked them regarding white settlers. (Bear in mind most encountered the French more often than anyone) It was a religious thing, and prudent in a hunting culture. Bathing was considered healthful, even on cold days, and a sign of strength and vigor to others, not unlike Nordic culture. One southern chieftain, taken to France for the purposes of impressing him and his entourage for trade negotiations, was asked on his return to New Orleans what he thought of Paris, the buildings and the people. He responded to the journalist of the local Orleans paper something like this, "It was very impressive, but the women smelled like alligators."
Midwestern and southern Indians showed the settlers how to use soapweed (yucca) to wash hair and body... evidently they weren't to impressed with lye soap, which was quite caustic if the balance wasn't just right. Another reason whites were reluctant to bathe, as well as the English, German and Scottish settler's belief that bathing was unhealthful and caused illness. In a way they were right- settler's homes were cold, not cozy, and they could indeed get pneumonia. The natives' winter houses - they often had open air pavilions in summer- were smaller and better suited to the cold. Most settlers couldn't even swim, since they viewed water as unhealthy, perhaps a holdover from populous Europe where the wastes went into the water and it WAS unhealthy. Everyone, even children, drank cider, dairy or beer, rather than water, when given a choice.