This a cool idea to display the data, but as-is it's nearly impossible to read. Like, if I want to follow a year's snowfall chronologically, should I be zig-zagging down a column or reading in short rows right-to-left?

At least for an English-speaking audience, I think it would work better if you flipped it so the years are rows and the months are columns, and keep all the snowfalls for one month in the same row. Will be a lot more intuitive to read right-to-left. To keep it from getting too spread out, you'd have to do something like spacing the snowflakes in their month based on % of the way through the month rather than having space for 30 individual days. Kinda like this, but not shit because you actually know how to use Tableau.