In this context, the term "jade" means a very tired horse. This is a secondary definition of "jade," related to the idea of being jaded. It isn't common in speech, but it is fairly common in literary writing to refer to exhausted or worn out horses as jades.
Now, to get the full meaning, you have to put that word in context. Here Shakespeare refers to jades who "drag the tragic melancholy night." Soon after he mentions wings. Think of all the mythic images of flying horses/winged horses drawing chariots and you're on the way. This is a dark coach or chariot, something like the chariot of night and perhaps death (look at the lines following). These exhausted horses pull the night slowly on, breathing out sickness. This is part of Shakespeare setting the stage, evoking a nightmare image.