You're probably already familiar with the word "trap", like the kind used to catch mice but in Shakespeare's day the word "trap" could also mean something else. This second meaning of trap came from the Latin word "drappus" which meant a piece of cloth. Which is why it is also the origin of our word "drapes." In this case, the word "trap" referes more specifically to the fancy, decorative coverings on a nobleman's horse. So, when the Lord says "Thy horses shall be trapped," he means they will be decorated in a way that shows Sly's noble status.