Not only do they exist, but you can see them at most major zoos. You have to keep in mind two things:
1) The same people who described them as a horse with a horn also described a hippo as a “river horse.”
2) Unicorns were said to have massive, thick legs and feet like an elephant, super-tough hides, and were extremely rugged.
3) The horn grew out of its nose, not its forehead.
Now, what creature looks no more unlike a horse than a hippo, has a massive horn on its nose, has legs and feet like an elephant, is built extremely ruggedly, and has a thick, thick hide?
The fairy-tale girly horses are the imagination of someone who read no further than “horse” and “horn.”
That's right. The House *and* the Senate.
And also keep in mind that people did not have glasses in those ancient times and might have seen something that appeared to be a unicorn but was something else entirely.