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This is how I would make a unicorn horn.
Go to the Dollar Store and buy the large, spiral, holiday Icicles they sell. I think they plastic, and they are not heavy. I have seen them 6 – 8 inches long.This will be your "horn"
File the base of the wide end flat.
Using a hot glue gun, glue they base of the horn to a heavy piece of cardboard for support. Figure it should be about 3" square. Clamp and allow it to dry.
Then incorporate it into your headpiece. They way I would do this is to fashion a small pocket into the forehead of the headpiece fabric. Insert the horn/cardboard base, close the flap and stitch around it to secure it into place.
Because the horn is made of lightweight material, you should have no problem supporting it in the headpiece.
Hope that helps.

I made a unicorn costume once.

Take card board and form it in a triangle. Stuff the middle with stuffing then sew the surounding triangle with a nice white or whatever color cloth you want. and then put elastic or velcrow attatched. and vala you have a horn.

Go as a "rosenback" rider and horse in the Circus you in a sparkle suit and horse with surcingle and plume! Add some glitter to her tail!