Albert Barnes' Notes on the Whole Bible - Deuteronomy 17:16
The horse was not anciently used in the East for purposes of agriculture or traveling, but ordinarily for war only. He appears constantly in Scripture as the symbol and embodiment of fleshly strength and the might of the creature (compare Psalms 20:7; Psalms 33:16-17; Psalms 147:10; Job 39:19 ff), and is sometimes significantly spoken of simply as “the strong one” (compare Jeremiah 8:16). The spirit of the prohibition therefore is that the king of Israel must not, like other earthly potentates,... read more
The Pulpit Commentary - Deuteronomy 17:16-17
Certain rules are prescribed for the king. It is forbidden to him to multiply horses, to multiply wives, and to amass large treasures of silver and gold, and he must have a copy of the Law written out for him from that kept by the priests, that he might have it by him, and read it all the days of his life. The multiplying of horses is prohibited, because this would bring Israel into intercourse and friendly relations with Egypt, and might tend to their going back to that country from which... read more