The text implementation of the races looks great.
The game description gives the impression that the simulation of the race is pretty detailed (probably why the same horse never stays in first place all the way, which helps a lot in making the races exciting), but as a player I would have liked to have more information in the game itself (for example, knowing in advance what kind of race the next race is going to be to train accordingly). Obviously in a jam you don’t always have time to do everything.
Maybe naming the rivals could help create some tension across various races. Getting to name your own horse is also always fun :)
Overall it’s a pretty fun idea for a game. Good job!