This is a well-written, easy reading, fast-moving story.
The major problem I see with it is you have made separate paragraphs where they were not necessary, and there is no indentation.
Example: Your story: As exercise riders, we usually have the job of riding the jumpers out to the schooling field and warming them up for the jockeys. Then we switch horses. The jockeys would school the fresh set of horses over the fences, as we rode the already schooled horses back to the stable. This is what I did that day, until the boss asked me to bring the horse I just brought out to see jump with the other two jockeys.

Normally the schooling session goes as follows; Riders bring their horse up to the first jump and stand, letting the horse look at it, while the boss spoke about how he would like the school to go. The riders would agree on the plan and ride back far enough to get a straight start to the jumps. The boss would then follow the group in his car as they ran at full speed over three of the full size race fences together.

So, when the boss asked me to let my horse come look at the jump I questioned when I was to switch horses. He said we were not switching, that I was schooling this horse. I felt a number of feelings at this time and there was no time for questioning. I was schooling this horse and that was that. As the jockeys turned to get a running start and the boss got into his car, I had no choice but to follow and do as I was told.

My Suggestion: normally the schooling session goes as follows; Riders bring their horse up to the first jump and stand, letting the horse look at it, while the boss spoke about how he would like the school to go. The riders would agree on the plan and ride back far enough to get a straight start to the jumps. The boss would then follow the group in his car as they ran at full speed over three of the full-size race fences together.

So, when the boss asked me to let my horse come look at the jump I questioned when I was to switch horses. He said we were not switching, that I was schooling this horse. I felt a number of feelings at this time and there was no time for questioning. I was schooling this horse and that was that. As the jockeys turned to get a running start and the boss got into his car, I had no choice but to follow and do as I was told.

My Suggestion: Normally the schooling session goes as follows; Riders bring their horse up to the first jump and stand, letting the horse look at it, while the boss spoke about how he would like the school to go. The riders would agree on the plan and ride back far enough to get a straight start to the jumps. The boss would then follow the group in his car as they ran at full speed over three of the full-size race fences together. So, when the boss asked me to let my horse come look at the jump I questioned when I was to switch horses. He said we were not switching, that I was schooling this horse. I felt a number of feelings at this time and there was no time for questioning. I was schooling this horse and that was that. As the jockeys turned to get a running start and the boss got into his car, I had no choice but to follow and do as I was told.
This paragraph is about the jockey. Therefore it is one congruent paragraph. It flows smoother this way.
As always, this is only a suggestion. Using is entirely your decision.

Good luck with your future writing projects.