I don't know why this is important but here you go. Horn is made up of two things. A "bony" core and a keratin cover. This structure is fed by blood vessels at the base.
Think of dehorning when a calf is very young and a hot outer ring hollow core iron is used to burn around the bud. This kills the horn searing off the blood supply and then the bud falls off. If a poor job is done, then a scur may grow, but that is easily removed. If the bud is turning into a horn, usually at two months when the bud becomes "bony" and attaches to the skull, then a surgical method is required. I always dehorned a few days after birth as soon as I could feel the buds. The bulls also lost their bull hood at the same time.
Now does the inner bony structure of the horn recess with age? I say no because if this occurred, then the outer keratin layer would fall off. No way the keratin layer could shrink since it is similar to fingernails. Without the outer layer, the inner bone would not exist.
Cattle horns grow the entire life of the bovine, however, most of the growth is seen in the first 6 years or so.
Here is the photo of a horn tip I saved off an old cow You can see
the "bony" center. The tip of the horn always stays solid while the
"bony" structure between it and the skull is porous as seen in the