I thought all antlers fell off each year, if they don’t fall off then they are horns.
From Wikipedia (the most reliable source on the interweb)
Antlers are extensions of an animal’s skull found in members of the deer family. They are true bone and are a single structure. They are generally found only on males, with the exception of the caribou. Antlers are shed and regrown each year and function primarily as objects of sexual attraction and as weapons in fights between males for control of harems.
In contrast, horns, found on pronghorns and bovids such as sheep, goats, bison and cattle, are two-part structures. An interior of bone (also an extension of the skull) is covered by an exterior sheath grown by specialized hair follicles, the same material as human fingernails and toenails. Horns are never shed and continue to grow throughout the animal’s life. The exception to this rule is the pronghorn which sheds and regrows its horn sheath each year. They usually grow in symmetrical pairs.