http://www.straightdope.com/columns/read/248/whats-the-origin-of-horny
I thought the term originated with the rutting season for deer, elk, moose and other antlered creatures. They have new horn growth during that time and are obsessed with sex. Much like human guys, except we don’t have antlers and we are obsessed year round. 
No, the OED shows that it derives from “horn,” “An erect penis; an erection. Also in phr. to have (get) the horn, to be sexually excited.” The OED traces “horny” to 1889 and “have the horn” to 1879 - 80. So Cecil’s answer is essentially correct, though lacking detail. I don’t know what is the basis for Cecil’s claim that the term dates from the 15th century.