As others have said, the article a in that sentence is modifying the word storm, not snow.
That said, it's worth pointing out that we can use an indefinite article before the word snow, even when the word storm doesn't follow. A bad snowstorm is often called a big snow, even without the word storm:
We had a big snow in December, but the warm winds have melted most of the snow in the low range of mountains here. (Climatological Data for the United States by Sections, Volume 7, Jan. 1920)
We had a big snow the night before that last game and it was like playing on concrete. (Todd Mishler, Blood, Sweat, and Cheers: Great Football Rivalries of the Big Ten, 2007)
In Grandview, when a big snow came, it was a wholesale holiday for everybody. That way folks stayed safe, warm, and dry. (Robert Hill, The Color of Sabbath, 2007)
Similarly, we can say:
We had a huge rain on Sunday, which has caused the river to rise.
In contexts such as these, phrases like "a big snow" and "a huge rain" are acceptable, shortened ways of saying "a large amount of snowfall" or "a huge amount of rain."
You are right when you say that snow is not a countable noun. But you are wrong if you think that all mass nouns can never be used in a countable context. English is too flexible to adhere to such rigid rules.