I start every costume creation by finding an example that is done often, but not to an extreme level. I saw that the only unicorn costumes online were baggy store bought suits or a horn duct taped to someone’s forehead. I knew I could do better and add an X-Factor like fog snorting out the nose.
Create your foundational foam structure. I recommend using a combination of the dense core home foundation insulation and expanding foam (low expansion and high expansion). Cut the foam by scoring and breaking. Glue it together with Gorilla glue and definitely use clamps. You can insert pieces of wire at this stage to reenforce joints. Don't rush the gluing process and let it cure for a solid day or two.
You can then use your expanding foam to get a bulk structure for rounded areas.