It was 8 or 9 years ago so I don't remember it super well, but it's mostly cardboard and papier mâché. I built the base using cardboard boxes and a lot of masking tape, and you can still see some of the tape and cardboard inside the snout.
I made the horns by cutting 2 identical spiral shapes out of cardboard, and stretching them like a slinky, which is a much easier way to get them to spiral and be symmetrical than starting out with a straight thing and curving it. I'm pretty sure I bulked them up and got them to stay in that shape by taping lots of wads of crumpled up newspaper to the sides.
I covered the whole thing in layers of very cheap paper towel and Elmer's art paste, and used that to add a few little ridges and such.
The texture on the horns was made by just wrapping one long continuous strip of paper towel around and around, straight off the roll. (It was the really cheap stuff with no perforations and with obvious flecks of recycled paper in it.)
I have a piece of polyester batting shoved into the top because I didn't quite get it to the same shape as the top my head, and it's a bit uncomfortable.
It's also very hard to see in! I looked at photos of real sheep skulls for reference, and I put the eyes further forward to account for my human binocular vision, but they're still really far back and hard to see out of, so you have to look out the nose too.
I seem to remember first painting it with glossy acrylic paint, and then repainting it with matte paints because it just doesn't look as skull-like when shiny. The shading is awful because acrylic paints dry so dang fast, so it might be nice to go back and refine the texture a bit and repaint it again someday, but that's not at all on my priority list right now.
I hope this helps, and that you have fun making one!