It's very probable that there's no rider who doesn't fantasize about his own horse. A horse running form pasture directly to you as soon as it sees you, because it knows that you and you alone always carry his carrots in your pocket...
Let's talk about horse psychology, just so you get an idea about what is to be expected on this path named "owning your horse". When you keep horses like I do, free all year round, you realize what's important to them and what do they throughout the day. Horses are most interested in food (they spend 16 hours daily just eating), then sex, lucky for you, it's only once a year :)), then they put much thought in hierarchy. It's very important for an average horse to get out of the stronger horse's way and to pick on those weaker than himself. Horses have their friends and their enemies. And they constantly try to improve their hierarchical position. Horses do it with other horses and with riders. If you don't respond with a scandal to horse's tries to impose on you, a fairytale will soon turn to hell.
The female part of population shares this collective illusion that goes something like this - if I cuddle my horse, feed it with carrots and love it very much nad bathe it every day with scented perfumes and similar nonsense, then it'll love me too, and carry me on it's back. Right. The truth is as follows. If you wait all the time for a horse to make a mistake to get the chance to pick on it (for example, you give it a clear signal to go througa a puddle, and it goes around it, then you should make it go through it not once but three times and if possible, make it stay in that puddle until you give it a command to go out), then a horse will recognize you as a stronger person and obey you blindly.
The bad side of having horses is that you have to force them in everything, the good side is that you can force them on anything. With a weak (in a psychological sense) rider, a horse won't go through a puddle, but the same horse would jump off a building with a strong willed rider, and after they've both looked over the edge how far is the ground. So, the magick formula is first to force a horse and harass it for every try to impose on you, and when it's good and obedient, then you get to reward it with apples or carrots because they love to eat most, altough massage gives good ressults too.