“He should not have an abundance of horses!” (Devarim 17:16)
It is a negative commandment that the king should not have too many horses, apart from those that he needs for his chariot and for his cavalry. This is said clearly in the verse “He should not have an abundance of horses!”
The idea behind the commandment is that he should have not have horses which run before him for honor only. This commandment is transgressed even if the king has only one extra horse. If, however, he has horses in his stables ready for battle and sometimes his cavalry will ride on them, this is not included in this prohibition at all, as the idea is only that he should not have wasted horses running before him only to honor him. He should have only enough for his own chariot.
The verse itself is explicit in the reason for this commandment, as the verse says “and he will not bring the people back to Egypt in order to have an abundance of horses”, which means that it is so that he should not send members of his nation to Egypt to live in order to raise horses there (as the prohibition against living there is only about fixing one’s abode there), and also so that he should not become haughty when he has too much gold, silver and horses, for horses, because of their beauty and swiftness are animals about which there owners show off.
This interdiction applies when Eretz Yisrael is inhabited with Klal Yisrael and we have a king. It is one of those commandments which apply only to the king. A king who transgresses this prohibition and adds even one extra horse to run in front of him in the way that the kings of other nations do, deserves lashes.