After the horse refuses to take on the saddle, click on the horse and go to reinforcement. Select 'scold for…' and then the option for refusing to be saddled should come up. Every time the horse refuses to be saddled, do that, and that should eventually make it trained, I think lol. Still kind of new to Pets myself but that should be how you train the horse.
A little explanation how trait training actually works:
From my observation, the traits have numeric ratings on them that you can't see, and there are specific values that will determine what trait they have. There is a trait on one end of the spectrum that emulates poor behavior, and on the other end of the spectrum is a trait that is it's direct opposite. In the middle, there is a range that indicates that the pet has neither trait, or a neutral value.
Reinforcement is not the only thing that changes this rating: the act of participating in certain behavior will change it, too...just not as much. Doing something that is in line with a good or bad trait will change that rating in the direction of the appropriate trait. Reinforcement changes the rating by a lot more in the direction of the trait relating to the reinforcement being applied. Thus, scolding your pet for a specific behavior will still be a net gain in the direction of the of the reinforced trait. However, praising your pet for desired behavior will be a larger gain in the desired direction.
The Destructive trait is one that I've dealt with the most, so I'll use it as an example:
You have a puppy with the Destructive trait, which makes it more likely to autonomously chew furniture. The puppy chews on a dining room chair, and you give no reinforcement. The rating of the Destructive/Non-Destructive trait moves slightly to the Destructive side. The puppy chews on a dining room chair again, but this time you scold it for being destructive. The rating moves slightly to the Destructive side of the scale from the act of chewing, but moves
more to the Non-Destructive side of the scale after you scold it. As an end result of the latter scenario, it is closer to the Non-Destructive side of the scale than it was before it chewed.
Now you decide to buy your puppy a toy box, and you make a chew toy available to it. The puppy goes and chews on the chew toy and you don't praise it for doing so. It gets a boost towards the Non-Destructive side of the scale. It chews on the chew toy again, but this time you praise it for being Non-Destructive. It gets the boost from chewing
and the boost from being praised, both in the direction of the the Non-Destructive side. Praising it for chewing on the chew toy is a bigger boost than scolding it for chewing on the dining room chair, because both boosts are in the desired direction. As a player, you can even direct the puppy away from destructive behavior by cuing up a "chew toy" action when it's Destruction need gets low, and then have a Sim praise it for doing so, and speed the process up greatly with a minimum of scolding.
As the reinforcement continues, the value will drop below the minimum for the destructive trait. At this point, it loses the Destructive trait, meaning that the dining room chair will not be it's default choice for a chew toy (it's not out of the question, either). However, this value is not high enough yet to give it the Non-Destructive trait, so it simply has no trait on this particular scale. It basically has no particular preference, and is just as likely to chew furniture as it is to seek out a chew toy. Thus, you have to keep up the above procedure. Before long, that value will rise to the point to where it gains the Non-Destructive trait.
However, this just means that it will be more likely to seek out a chew toy than it is to vandalize furniture. If there are no toys available, it will still want to satisfy it's need for Destruction, so the chair is the next best thing. There's even a small chance that it just decides that chewing the chair would be perfectly OK
this time. Unless this reinforcement is continued even after it gains the desired trait, it will revert to old behavior. But the closer it is to the end of that scale, the longer it will take to revert.