How do those grates do in the snow? I'll bet the design is supposed to have the snow drop through the grating, keeping the roadway clear.
If it works, it's a great idea.
I doubt snow but think its for aerodynamics - to keep the bridge from flying in high winds - like Galloping Gertie did over the Tacoma Narrows.
As I recall, the reason was both to prevent snow/ice build up, and because of the winter winds that whistle through the straights. (They didn't want a repeat of the Tachoma Narrows bridge.)
Reportedly, the winds are sometimes strong enough to lift vehicles. (In 1989, a 31-year-old woman was killed when her Yugo was blown off the bridge.)