Create the basic shape for your horns using aluminum foil. You can make them long and curvy if you want, but too many tight twists will make the foil difficult to remove later on. I went with a basic goat-horn shape.

Wrap the horn forms in saran wrap. This will keep the outer layer from sticking to the foil.

Cut up one or two paper towels into small strips. Squeeze some wood glue onto a disposable surface. I'm using Titebond III - this is one of the strongest and easiest to work-with glues out there. It takes a while to dry but is really strong, and the resulting material feels a bit like leather, with a slight flexibility to it.

Mix a little water in with the glue using a paint brush or stirrer you don't care about -- this stuff is hard to get out once it starts drying. Just add enough water so the glue is a bit runny and more like a paint consistency than a glue consistency.

Dip the paper towel strips in the glue mixture and smooth them down over the form, rubbing with your fingers to obscure any obvious edges. The paper towels soak up a lot of glue so you can keep the paper mache fairly thin. This glue will dry very strong, so don't use more than 1-2 layers. The thicker it is, the less light will get through.

Let them dry for at least 24 hours.

The paper will dry a darker brown color, which to me looks just like goat horns. They also have an interesting texture, thanks to the paper towels. They are sandable and paintable, so you may add details and shading if you like, but remember that an opaque paint will also block the light transmission, so be sparing. I'm really happy with the way they look with no paint whatsoever.

Peel the adhesive off the back of the LED strips and insert them into the horns with the lights facing inwards, so the whole horn illuminates. You'll want to stick the lights firmly to the back wall of the horns - so spend a little time deciding which way they'll face on the headband before you commit. 

The adhesive on the strips is helpful for initial placement but won't hold up to longer term use. These strips really look best when they're stuck to one wall rather than "floating" in the middle - if the front side of the lights get too close to the edge you can see the individual pixels rather than the diffused glow.

Test them out with the animations by shaking and tilting the board. You can change the brightness of the LEDs in the code, and tweak them to get exactly the look you're going for.