you're sentences are correct but The regular way to say it would be "the traffic stopped because of the snow."
saying "failed" and "paralyzed" could be correct, but only if you want to sound very dramatic which is probably what Lizzy means when she said they don't really fit. Because those are very serious words if you know what I mean.
"due to snowfall" is also correct, but it's extremely formal and as a matter of fact, I only hear that phrase from the weather man haha : ) . I would also just say "snow" instead of "snowfall" because saying 'snow' is sufficient, and again I only hear the word "snowfall" fro the weather man.
But again- both of your sentences are correct and very well translated, they're just very formal/poetic/dramatic.