No pun intended, the misconception started as a minor mistake and was victim to the snowball effect. It began because of Franz Boas. In 1911, Boas wrote The Handbook of North American Indians.
He discussed how there are many different terms different cultures and languages have for the “same thing.” Using English as an example, think of how many terms we have for water: rain water, salt water, fresh water, rain, foam, wave, lake, puddle, pond, river, lagoon, waterfall, etc. All of them refer to different things that can all be generalized as water.
In fact, you could probably back up a claim that English has 50 terms for water (please, don't attempt to list them in the comments). Boas gave four examples like these for how the Eskimos referred to snow: “snow on the ground,” “falling snow,” “drifting snow,” and “snow drift.”
This work was left alone until Benjamin Lee Whorf made a small mistake with the facts in the 1940’s. He said that we have the same word for all kinds of snow (despite the fact that we use terms like hail and sleet) and that Eskimos use many words for snow.
In 1958, Roger Brown quoted Whorf, further distorting the truth and increasing the number. After Roger Brown, nobody went back to Boas’ original writing and the reality became more and more distorted (here, the snowball effect) until Lanford Wilson claimed there are 50 words for snow in the Eskimo language in 1978, unintentionally spreading the mistruth we know today.