I’m so far behind that I hadn’t read it yet when this thread started, but the 21 June issue of Science is a special issue on ruminant genomes.
From what I’m reading, the ruminants’ boney outgrowths, which range from horns to antlers (including pronghorn’s pronghorns and giraffe’s ossicones) probably evolved once in either a common ancestor to all ruminants or in one that excludes mouse deer (which don’t have antlers.) Musk deer don’t either, but they’re thought to have lost them. The genetics are complicated, involving over 200 common genes, plus another 600+ specific to horns and 700+ specific to antlers.