The only thing I've rubbed on these Dall Sheep horns for the past 22 years are my hands. Kind of a nice thing about a set of horns.....you can grab them whenever and fondle them, unlike a mount up on the wall.
I think as long as the horns aren't exposed to direct sunlight in your trophy room, you don't have to put anything on them. Wipe the dust off with a damp rag every so often.
Yeah Pat, those horns do look a little "grimey".
The sun is hard on horns wither they are in your trophy room or on the animal in the wild. In the wild, the animals rub their horns (and antlers) on trees and bushes, and the sap from those trees puts moisture in the horns, and gives them a darker color.
The Montana rams that I have shot all had fresh pitch or sap from conifer trees on their horns. I remember their horns smelling like a fir tree.
The surface of horns dry out over time and become lighter. I've found that an occasional light application of furniture oil on the horns and antlers restores the moisture in the horns and brings back their original color. If you put too much on, just wait a few months, they will dry and become lighter. Just don't use any kind of varnish. Over time, layers of varnish build up, turn yellow, flake off, and all kinds of un-natural looking things.