It's a cliché among journalists rather than a theory among linguists.
According to that Wikipedia article, it's the Sami languages that have lots of words for snow, though it all critically depends on what you mean by "word", "snow", "language", "have", ... The question "How many words for snow does language X have?" is impossible to answer for many different reasons.
You're right: the answer for Dutch or German would be 'infinite' because these languages allow you to compose (new) words on the fly, using other nouns as prefix.
The first example I came up with after 0.05s of thought was "autosneeuw" (car snow) which could mean the snow you find on top of a car.
According to that Wikipedia article, it's the Sami languages that have lots of words for snow, though it all critically depends on what you mean by "word", "snow", "language", "have", ... The question "How many words for snow does language X have?" is impossible to answer for many different reasons.