Many animal 'horns' are made of a-keratin which is the same stuff that forms hair, claws and fingernails. Strictly speaking these are not classed as horns. As these keratin cells die they harden and then special sections of the skin transform the keratin into a horn (or claw or fingernail or hair, depending on the special skin cells.) Keratin is a protein and its chemistry will vary a fair bit. The keratin usually covers a core of living bone. A link can be found below to check facts and assist an investigator in learning more.
Horns are properly made from bone.