What term describes animals with unbranched horns that never shed?

The term that describes animals with unbranched horns that never shed is "horned mammals." Unlike antlers, which are branched and shed annually, the horns of horned mammals are composed of keratin and bone, and they are a permanent feature of the animal. This term encompasses various species that possess these characteristics.

Grazers and browsers refer more to the dietary preferences of certain herbivorous animals rather than their physical traits, specifically the structure and nature of their horns or antlers. Grazers typically feed on grass, while browsers prefer leaves, shrubs, and trees. Cervidae is the scientific family name that includes deer, which are known for having antlers, not horns. Thus, "horned mammals" is the most accurate term to describe those animals in this context.