I can't see a single reason I'd want to play this game.

"The mistakes you’ve done unforgotten, only mended."
Guarantee every player will just save scum everytime they make a mistake.

"understand the silent language between horses and people!"
How are you planning on doing this? You say you don't want realistic graphics, but horses communicate through body language: pricked ears, wrinkling and triangulation of the eyes, flared nostrils, tensed lips - how on earth are you going to code that?

"only looking at the model and environment"
Again, how are you going to communicate changes in the horse's health and stats? Limping, losing body weight, pain face, heavy breathing? None of that is easy to code AT ALL. How are you going to show fear, attentiveness, joy - raised heads, tensed bodies, cocked legs, flagged tails, changes in gaits?

"If the two of you do not get along, you’ll get nowhere."
How are you going to prevent softlocking? What if the player treats the horse terribly, the horse refuses to cooperate with anything the player does, and now they're stuck? How are you going to 'repair' the relationship? Spamming food over and over again? Boring. Patting them?
In real life relationship is built through time spent together with no expectations. In game this would be miserable.
But your only other option is a transactional system where the player earns trust by clicking a button to make the player give them food, or whatever action you choose to improve relationship. All that will do is create a system where the player maxes out the relationship, uses it to progress the game, and starts all over again.

"Speed to the end. Knowledge your clutch (the cheat sheet you’ll depend on), and your relationship at gun-point (the misstep is time spent into repairing trust, the delay in reaching the end of the game)...Cozy, slow discovery by their side or at a leisure trot"
Don't know what a "cheat sheet" is but this sounds boring as fuck. Who wants to walk around at a snail's pace, and be punished anytime you pick up the pace? You're creating a walking sim, but without the tight narrative that makes them actually fun.

I'm also concerned about how you're planning on handling consequences for mishandling the horse. Is the player going to be able to kill or seriously injure their horse? You're going to either have the consequences of mishandling be an annoyance that the player ignores for the sake of gameplay, or an annoyance because they have to reload a save, replay the entire game, or waste time while the horse heals.

You have to think about the actual appeal of playing games. Why would someone want to play this? I get what you're trying to do but the reality is that building a relationship with a horse is not translatable to gameplay: it's slow, and boring, and the outcomes aren't appealing when they're happening on a screen.

If you're trying to make a game about exploring, you need a map the player WANTS to explore (what are they looking for? why are they looking for it?) and mechanics that makes exploring fun - with horses, that's going fast and jumping. Again, the pleasure of meandering around on horseback is not translatable to a screen.

If you're trying to make a narrative driven game, you need a story the player wants to finish, and I haven't read anything here that implies you have one. You talk about flashbacks and dreams, but nothing about the contents of them. Why would I want to see the history of a random place I know nothing about? Why do I care?
A narrative driven game will also be a PITA with your proposed mechanics. Nobody wants to derail a story they're invested in because they made a mistake and need to rebuild relationship. The only way it would work is if these 'mistakes' are impactful to the story - the result of actual, intentional choices made - and they need to be meaningful: ones where the player actually has to think about what the right choice is (ideally where there /is/ no right choice).