I think the frequency of a horse getting worked up before a race depends a lot on its disposition. I manual train and I have always set the training emphasis to Stamina. This tends to turn a lot of my horses disposition to Laid Back which usually translates to my horses being relaxed before a race. Your head lad will tell you if your horse needs a pacifier. Whether he tells you every time a horse needs a pacifier I don't know. Maybe he misses a few? Figuring out what pacifier will work with your horse is a guessing game.
Check out the legend editor in the game to get an idea of how the game creates a horse and all of its variables. Hover over each category for an explanation. It will help you to figure what is going on.