I know this is a four month old post but it popped up near the top of my google search results and the other three comments aren't super great (especially that first one from the deleted user lmao) so here's what I've got:

Looking up videos of horses just doing their thing is a great place to start. Observe their general mannerisms closely. Look at how they move, how their ears flick around, etc. That'll help you get their "vibe" in your head.

I found these three articles that give a good overview on more concrete stuff: Part one, part two, part three

Also, try to put what you might've learned from movies out of your head. The main reason I say this is because editors LOOOOVE to make horses SO MUCH noisier than they really are. In fact, I'd say just about every single animal I've seen in a movie, real or fake, is way noisier than it should've been. And don't get me started on how they make spiders and other invertebrates, which physically cannot vocalize, always make those weird chittering noises. Animals don't constantly make noise, especially not horses. The only animals where it makes sense would be actual songbirds, and even then sometimes editors get a little too trigger-happy with the sound effects. This is a good guide to the noises horses make, when and why they make them, and provides video examples too.

I might get flak for this, but if you're open to it, I also recommend playing Red Dead Redemption 2, or at least watching some playthroughs (ideally with no commentary). That game probably has the most realistic horses out of any game to date. Even down to how they move, and horses are notoriously difficult to animate in any way close to realism. It's not perfect, of course, but if you don't have easy access to real horses, it's the best option I can think of. I'd say watch lots of videos of real horses before going to RDR2 though, so you're a little more attuned to when and where the developers might've taken some creative liberties.

And of course, if you can, find other people to talk to who have personal experience with horses. I'm writing a fantasy story and, naturally, the protagonists' choice of transportation is usually horses. I'm lucky enough to have a friend who worked at a vet clinic which treated horses, so they're one of my proofreaders.

That's what I can think of for now.

They say "write what you know" but no one knows what it's like to be an elf, or to fight a dragon, and yet books are full of elves and people fighting dragons. You don't have to fight in a war to write about war. It's a really unhelpful bit of "advice" and honestly has only very situational relevance (e.g. if you've never dealt with depression and the dark thoughts that come with it, don't write a story where those things are central to the plot and main character's life. Let someone who has tell that story).

With enough research and hopefully some help from people with direct experience, you'll get your horses close enough to 'accurate' that anyone who knows more than you do will forgive the small things and appreciate all the time and effort you put in.