A unicorn is not a horse!?

As a fan of fantasy films I just find it really annoying that in this age of wonderful CGI technology, film makers still insist on sticking a fake horn onto a pretty white horse and ping it off as a unicorn. As far as I know.. a unicorn is not a horse..it is supposed to be a creature made up of something like, the head of a horse with the obligatory horn, the feat of a goat, the tail of a lion ( I'm no authority or anything). If they can produce a decent hypogriff in Harry Potter, why can't they produce a decent unicorn..eh?