Jamieson, Fausset and Brown on Deuteronomy 17:16

16. he shall not multiply horses to himself--The use of these animals was not absolutely prohibited, nor is there any reason to conclude that they might not be employed as part of the state equipage. But the multiplication of horses would inevitably lead to many evils, to increased intercourse with foreign nations, especially with Egypt, to the importation of an animal to which the character of the country was not suited, to the establishment of an Oriental military despotism, to proud and pompous parade in peace, to a dependence upon Egypt in time of war, and a consequent withdrawal of trust and confidence in God. (2Sa 8:4; 1Ki 10:26; 2Ch 1:16; 9:28; Is 31:3).