The idea that “Inuit” have a single language is evidently the first issue, but the idea behind the myth seemingly came from an 1800s anthropological study that mentioned four separate words. Many of the languages apparently have agglutinative qualities (like German, where you can just moosh more things on the end of a word to make a new one) as well as their cultures having a lot to do with snow (and thus likely having more jargon around it) leading to people running with ever-increasing numbers of words for snow that these “rudimentary” people had for “such a simple concept”.
English has more than 50 words for snow, so I don’t know why anyone would think it is a shock other cultures living where there is a lot of snow would as well. Of course some are slang and some marginal (hail is a type of snow if you squint enough). Snow is a very complex topic and people who live with it often need ways to quickly be more descriptive.
