When you reach out and tentatively pat a horse in its summer coat on the neck for the first time, what strikes you is “warm”, and “soft and silky”, quite different from cat or dog soft and silky. A horse’s summer coat is thinner and not as puffy as a cat or dog, without the feline/canine layers of undercoat and guard hairs. (I’m assuming your unicorn lives in a magical tropical forest where nobody ever has to grow a winter coat.
)
What strikes you about tentatively reaching out and petting a horse’s face–not the soft fleshy muzzle, but the long front of it, from its forehead on down, where the “blaze” markings if any are–is “bony”.
When petting a horse’s rump, what strikes you is “muscle”. That’s a whacking big muscle right under your hand, no doubt about it.
A horse’s mane, as noted, is quite coarse. Nobody pets an horse affectionately on the mane except little girls obsessively braiding it. 
You pet a horse affectionately on its neck, or on its muzzle, because that’s where it feels good to you.
If you pet a horse on its muzzle, ten to one it’s going to reach out inquisitively with its lips, on the not illogical assumption that there’s an edible treat there somewhere, and get slobber on your fingers. Children frequently panic and freak when this happens, snatching their hand away, thinking the horse is trying to bite them.
A horse’s hoof feels like nothing else on God’s green earth except a hoof. Think “humongous filthy Godzilla toenail”.
Horse manure does not smell too bad. Compared to cow manure, it’s less acrid, and actually not that stinky. Stepping on a few horse apples is not a crisis like stepping in a cowpie; it’s fairly easy to knock the clumps off your shoes.
Horses pee enormous puddles directly under them. “Pee like a racehorse”? Yup. When working with horses out in a dirt paddock, it’s not just the piles of droppings you have to watch out for, it’s also the mudpies where somebody peed.
Standing next to a horse for the first time, you are struck by an overwhelming physical sense of the sheer size of the beast. And you cannot imagine how anyone could lead it around on a string. Someone hands you a lead rope attached to his halter (the leather straps around his head), and says, “Bring him over here”. And you have NO clue how to proceed. You tentatively pull on the rope. “C’mere…” Nothing happens. You pull a little harder. “Hey. C’mere!” Still nothing happens. It’s like pulling a houseboat. His neck and head flex, but he doesn’t move.
Finally, somebody (giggling) points out that you’re standing directly in front of him, pulling on him, and if he did take a step, he’d step right on you, and not being stupid, he’s declining to do this. So the giggling person stops giggling long enough to show you how to stand alongside of him, facing the direction you wanna go, with your right hand up underneath his chin, holding onto the rope where it’s attached to the halter, and the rest of the rope in your left hand, and tells you to take a step yourself in the direction you wanna go, pulling his head along with you with your right hand.
So you do.
And he moves.
This enormously powerful beast is allowing you to lead him around by a string.
That’s a magical moment.
“Hey, he’s coming!”