Did the sun and moon symbolize fate in any of Shakespeare's plays?
Fate, in this usage, is defined as "the universal principle or ultimate agency by which the order of things is presumably prescribed" (Random House Dictionary).
It appears based on a couple of examples that sun and moon are not symbols of fate in Shakespeare. In Romeo and Juliet, the moon in the balcony scene symbolizes inconstant emotion and changeability, while the sun, or daybreak, in the wedding night scene symbolizes movement and activity and disclosure. In one example in Julius Caesar, it might be suggested that the sun, or a breaking day--"the Ides of March"--does symbolize fate as Caesar is warned to take caution on that day.