Sorry ... I just thought of something somewhat relevant to the care and feeding of horn.
I don't remember the exact year, only that it was between 1970 and 1973.
My mother and step father went Antelope hunting in ... Wyoming(?). Allegedly, my mum got one. (I strongly suspect my step pop is the one who actually bagged it, and blamed her.)
My mum could not hit the broad side of a barn - with a shotgun - while inside said barn. I watched her miss a spread out newspaper from 20 feet while trying to pattern her 12 gauge, using 3 inch "Squirrel and Pheasant" load, with number 7 1/2 shot, I believe it was. (she "borrowed" a few shells from me, to pattern her shotgun.)
If she really did bag that antelope, it was an accident/miracle shot ...
Anyway, they had the head (with horn) professionally mounted.
They moved to Missouri maybe 10 years later. Roughly 5 or 6 years after step pop passed, mum "donated" the mount (which by this time was in pretty rough condition, insofar as the hairy part was concerned) to one of the restaurants in town, to go with their deer, elk, moose, and fish mounts.
Mum and step pop never cleaned the mount or treated the horns or mount. As I said, the furry/hairy part of the mount deteriorated rather badly over the years. Developed a "few" bald and thin spots, it did.

The antlers on the other hand remained pristine. I would not be surprised if the restaurant moved the horns to a horn mount, and disposed of the head, since they received it.
Anyway, after at least 20 years with no care (other than
maybe an occasional dusting) (my mum was not big on dusting. She (rightly) considered it a waste of time and effort.) or treatment, the horns were fine. No shrinkage or cracking, at least not when I last saw it circa 1996.
So far as I know, the restaurant didn't/doesn't treat the horns on any of their mounts. (I have no idea if they have shut down between 1996 and now.)
It
may be that it is un-necessary to oil or wax horn, or do more than wipe it down with a damp cloth every once in a spell to clean off any dirt.