It depends on the kind of horn.
Antlers regrow each year; once grown and skin was shed, they're just dead bone.
Rhinozeros horn is dead keratin, growing from the base.
Bovidae horn is a living bony core, a very thin but living skin, and dead keratin; it grows in all areas, including the tip. (German wikipedia explicitly mentions the skin layer, English wikipedia does not.)
This kind of horn has inner air-filled chambers; these resonate. The chambers are lined with a mucous membrane, and take more and more volume with age.
For dead horn, it does not matter.
For living horn, air and humidity exchange will be affected. For large horns, this could become an issue. I'm no expert, so maybe there will not be serious problems, but if there are, this could be helped by applying the polish in patterns instead of as a contiguous layer.
Polish (or anything else applied to the horn) will also alter the resonance properties.