Your example is literally a horse with a horn on its head.
(Specifically, your horse looks like an Arabian horse with a horn on its head).
If you want to talk about fantasy unicorns, with beards, lion tails, and leg hair, that would once again, be the Episode horse with slight changes made.
“A unicorn is often depicted as a white horse-like or goat-like animal with a long horn and cloven hooves in the European folklore.”