Dont know if we are talking just the horns or if its a mount, but...... give them a good washing with dishwashing soap and a brush. Let dry for a few days. Mix 50/50 linseed oil and turpentine and give the horns a coat. Let it soak in and apply more in the areas that still look dry. After a few days, rub off any areas that have not soaked in.
Now for the easy way, especially if its a mount. Wash the horns off with a damp rag, cover the mount with a towel, plastic, or paper, and spray the horns with good ole WD-40. Do the same as above, letting them soak and re-apply as needed.
Good luck and let us know how they come out.

Need some help on how I can clean a Exotic Ram mount. It has gotten very dirty looking sitting on my wall for many years. Is there a method I can use to freshen it back up.
Thanks
Bobga