I agree with Endiku, go into the history of equestrianism, where it originated, how it spread, etc.
Can you talk about when you got your first horse? And then start talking about the first people to ride horses, what they did with them?
Intro: mention your first horse (don't get all enthusiastic about how he just learnt flying changes or anything, just give a brief overview of your own horsey experience), then 'go back to where it all began' with whoever it was that started riding (think it was the Mongols?) and give a very basic intro into how their society was based around horses and the like.
Paragraph 1: talk about your 'first horse' experience. Talk about what happened, what you did with him, how you introduced him to his new home, etc. Just basically about you and your horse.
Paragraph 2: talk about the first horse people. Talk about their 'first horse' and how/when/why/where they were originally tamed. What were they used for? What had they been used for previously? How did this influence their culture? Did it help them to advance (say that it did) and how? What changed in their society to accommodate for these horses?
Paragraph 3: talk about how your horse has changed YOU. Just as the Mongols changed because of the horses in their lives, so has yours (again, say it has, even if it hasn't.) What have you had to change? How have you changed your horse? And how has your horse shaped you? What about you is now different? Are you more responsible? Independent? Assertive? What have been its positives? Are there negatives?
Outro: Recap what you've said before, basically. Mirror the intro.
As for a paragraph without 'I' too much...I think you're going to have to use 'I', because you're talking about yourself.
Here's what I would do, something like this: (I see you have a horse named Ace, I'm going to make up a bunch of stuff and just use his name, I don't even know if he was your first horse seeing as you have a bunch)
"Just as the Mongols changed their culture to adapt to the horses in their society, I have had to change too. With the arrival of Ace, I was suddenly learning to become more responsible, independent, and assertive. I was expected that, every morning, I would rise up to an hour earlier than the rest of the house so that I could feed, unrug, and groom my horse. The responsibility of owning such a large creature, which was fully dependent on my care, was one which weighed heavily on me. However, it also made me much more independent. I learnt to do all of these chores myself, and had to be reliable about them or my horse would suffer. Previous to owning a horse, I was sometimes lazy and quite a procrastinator. However, my horse experience changed all that. Every morning and afternoon, I went out to see to my horses' needs. I rode four to five days a week, and groomed, clipped, went to shows, saw to his medical needs, and was much more on top of things. I also became a lot more organised because of the responsibilities of keeping a horse. I learnt to be more assertive in my training of him, which is necessary because of their size and their nature. This carried over to other parts of my life and I found myself more confident of myself at school and other social events."
See how the 'I's just slip in, like a nothing word? Well they should, I tried my best lol.
^ all that might be rubbish. But this is just a sample.
Yeah sorry I went a bit over the top.
I love planning essays (is that weird?) but I absolutely hate writing them. Plus I'm struggling with my own at the moment so this is a welcome break from my own without making me feel like a slacker :)
ETA erm, I overdid it. But hope it helps!