Long, flowing mane. Lion-like tail. (The tail only is similar to those in these images: [2] [3]) Cloven hooves fringed by longer hair.
The horn is a single spiral horn in the middle of the forehead.
They have a palpable aura of magic, holiness and wildness that quite overwhelms any sense of ridiculousness at their gangling builds and those jolly unwieldy-looking horns. They never, ever 'feel' tame, even if caged.
Unicorns are never seen dirty or dishevelled unless captured or killed.
Unicorns are solitary with territories generally encompassing a forest. A resident unicorn is what enables other magical creatures (hobgoblins, boggarts, brownies, sprites etc - it hasn't yet been decided which of these are found on Larkspur) to live in the surrounding area.
There is a tradition, stretching back into legend and continuing into present times, of knights keeping themselves pure, going and finding a unicorn, and riding it on a quest. Generally when the monster is slain and the maiden rescued, the unicorn makes a hasty exit.
Unicorns are connected with purity in other ways: for example, they can purify water by dipping their horns into it, and indeed always do this before they drink.
Unicorns are not affected by any illusion magic native to Larkspur: you can't disguise one, neither can you fool one.
An imprisoned unicorn's aura changes to suggest a feeling of outrage and sacrilege to any onlooker.
Unicorns can be killed if you want to incur a godly curse on yourself and your entire bloodline. Once killed, they are usually dead.
The horn of a dead unicorn has no special properties whatsoever. A chip from the horn of a live unicorn has very many special properties indeed. Just watch out that the unicorn doesn't die while you're using your unicorn-ivory-tipped wand.