I lived there for 20 years, and there were a few cases where nearby areas got snow.
In 1988, Granada Hills got 2 inches of snow.
Around 1992, Valencia got a few inches.
But I never did see snow in Burbank or anywhere nearer downtown LA during that time; though LA has seen temps in the low 20's on rare occasion. I'm sure they've had snow previously... but it's definitely a very, very rare event.