Horns evolved in two families of mammals (pronghorns and bovidae; antelope types and sheep/goat/cow types), and in certain reptiles; if they evolved elsewhere they proved non-adaptive in predators. read more
Interesting question. I did not think about it until you have asked. So the question should actually be why even toed ungulates (Artiodactyla) have horns rather than why carnivores do not have horns. read more
Perissodactyls, with an odd number of toes, fall into three subgroups: horses and their cousins, the asses and zebras; tapirs, which don’t have horns either; and rhinoceroses. So the question isn’t why horses don't have horns, but instead why, unlike their closest relatives, rhinos do. read more