Adam Clarke on Deuteronomy 17:16

He shall not multiply horses - As horses appear to have been generally furnished by Egypt, God prohibits these,

1. Lest there should be such commerce with Egypt as might lead to idolatry.

2. Lest the people might depend on a well-appointed cavalry as a means of security, and so cease from trusting in the strength and protection of God. And,

3. That they might not be tempted to extend their dominion by means of cavalry, and so get scattered among the surrounding idolatrous nations, and thus cease, in process of time, to be that distinct and separate people which God intended they should be, and without which the prophecies relative to the Messiah could not be known to have their due and full accomplishment.