How does your fear influence your horse?
When we expect danger, our heart rate increases. It is one of our basic instincts: it prepares us to fight or flee from whatever is threatening us. This change is hardly perceivable to the naked eye, and we don’t even always notice it ourselves!
Horses, on the other hand, are able to sense these small changes in their handler or rider with no difficulty. They sense we are worried or scared, and respond in the same way: their heart rate increases and they prepare to flee.
Notice the difference: horses will rarely fight, they are programmed to flee! When you look at their anatomy, you will see that they are built to run: long legs and a massive chest to hold their enormous lungs. They are what we call cursorial prey: a species built to move (and used to being under attack of predators).

This horse is clearly not impressed by it's "scared" rider... You can't fool him!
This slight change in heart rate means they are ready to react, they are on edge. That is why, when the rider (or handler) is nervous because they know there is a bird in the bushes ready to fly away, or a dog in that one barn that always jumps up barking when they pass, that the horse often reacts much fiercer that usual at that point. The horse anticipated danger, because that’s what we were telling them was right around that corner!
If you are experiencing a lot more difficulty handling your horse at competitions or in situations you (maybe unconsciously) are stressed in, it might be worth looking into how you cope with stress, and how this influences your horse!
If you are interested in the research about this topic, Keeling, Jonare & Lanneborn did a nice paper about this in 2009, of which you can find the abstract here: https://pubmed.ncbi.nlm.nih.gov/19394879/ If you prefer, a nice summary was also written on the Science & Equine website, which you can find here: https://www.science-equine.com/articles/biomechanics-and-training/influence-of-the-rider/3763-investigating-horse-human-interactions-and-nervousness For some additional reading about the effect of riders on the heartrate of horses, I recommend reading this paper by Munsters et al (2012)! https://pubmed.ncbi.nlm.nih.gov/21612959/