Edited 03.02.23
Apparently throughout Hyrule, groups of wild horses roam fields freely. They come in an assortment of colors from blacks to reds and some even have patterns like dots on their flanks. Much like Hylians, horses have a variety of personalities and hidden strengths which makes each special in their own little way.
You had mentioned owning a horse yourself before during the walk to Hateno, although it's only upon leaving that Link got to meet her. A beautiful mare with black stretching up her legs and mane, although her body is a shining gray shade that appears almost blue in the light which must've been why you named her 'Celeste'.
It was clear from the moment Celeste came running after your whistle that your bond is a strong one. She was pleased to see her master again, nuzzling you with her muzzle as you explained to Link how he could get a horse of his own:
"Taming a horse requires patience. You wanna sneak up to them quietly. Beware that no matter what direction you approach from, if a horse gets spooked, their first instinct is to defend themselves, so be careful not to get kicked."
Link took a mental note of all the advice you had given him while leading him to the Blatchery Plains where a group of four horses graze on grass, blissfully unaware of any newcomers' presence.
"Now, when you get close enough, jump onto its back and hold on for dear life while trying to smooth it. Eventually it should calm down enough to realize you aren't there to cause it any harm," you give Celeste some loving pets before turning to Link, "Well, think you're ready to give it a shot?"
Watching the other horses, he gives an eager nod, excited to start building a relationship with a four-legged companion of his own.
"Which one are you going to choose?"
He gives it some careful thought, remembering what you had said about horses having different skill levels. Seeing that you'll both be traveling a long distance, he'll need a horse with good endurance and speed. The nearest one almost looks like Celeste just with white legs instead of black, however it appears to be on the shorter side and lazily saunters around the field in no big hurry. Not a good fit for a rough journey.
There's also two black horses, one pure and the other speckled all over with white dots. The ladder makes him feel dizzy simply by looking at it and the first seems like a nice fit until a leaf from a nearby tree drifts to the ground in front of it. Spooked, it sets out a loud neigh then runs off clear across the field, most of its herd following after it without question. Link's probably going to want a ride who's brave in the face of danger, not skittish enough to abandon him during battle.
While most of the herd circles the field in fright, there's one who merely looks up and shakes her head at such nonsense. This unbothered mare is a dark chestnut color with a light mane and tail. She's a brilliant creature, standing tall above the grass and trusting of her own safety, after all she knows she's powerful - powerful enough to stomp the most mischievous of bokoblins into mush beneath her hooves.
"That one."
You follow Link's point with a nod, "Alrighty. Good luck then and remember: be gentle and patient or else you'll make no progress towards gaining trust."
You leave him to it, watching as he carefully makes his way through the field while kneeled under the cover of tall blades of grass. As he gets closer to the horse of his choice, he slows his steps and keeps his breathing quiet before leaping forward.
Within seconds of feeling the new weight on her back, the mare stands on her hind legs, letting out a screech that alerts the others of trouble. Link, meanwhile, grabs onto her long mane, holding on tightly as she begins to buck around violently.

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Remember When...(Link x Reader)
FanfictionA hundred years ago, a group of Champions had planned and trained to fight Calamity Ganon. None of them could have predicted what actually ended up happening next: a betrayal from within leading to the destruction of Hyrule. After all those years...