Rawhide will work but so will thin leather, depends on you, leather is easier to work with, especially Deer hide, I'm going to talk Deer here. To use either make a paper pattern, start out with a flattened out cone shape. Once you get it close cut one out of leather wet it and see how it fits. Then, soak it and wring it, try fit it. Once you are close trim flat edges so there is a bit of a space between the two edges. Now you can punch the stitching holes. Take some waterproof glue, Tightbond II works and coat the the side that will be on the horn, while it is wet. Use a two needle saddle stitch, waxed thread, I start stitching going down through the first hole on either side then across to the next hole and come from underneath, pulling tight as you go. At the last two holes go though them twice, you can do this at the start also if you want, you'll have a double stitch. Take the needle points and push them back down through the stitching pull tight and trim off the tag ends they will slip back underneath the stitches and be held by the glue. Wipe everything with a wet rag and let it dry. Think of it like lacing you shoes and instead of tiring a knot feed the tag ends back down through the laces.
I would suggest practicing on a piece of scrap wood turned to a horn/cone shape. Sounds like a lot but once you get it it's pretty simple.
Tin and Pewter are a couple more options and two other stories.
Tim
Here is a Pic of how the patch is held on to dry:
This is the horn:
