All horses are sensitive, some are more so than others. And rightly so, horses are prey animals and being attuned to their environment meant the survival of the species.
Horses are immediate. They live in the Now, there are memories of what came before and anticipation of what comes next but neither is as important as what is happening Now.
A sensitive horse demands you be in the moment, not thinking about what to make for dinner or if you remembered to put the clothes in the dryer. To ride well you have to let go, clear your mind and focus on the Now. It is impossible to anticipate every spook, but you stay with your mount if you are riding in the moment.
No fear, no bullshit, no ego, just letting go and feeling your horse.
I think the best riders in the world all have the same trait, no matter their discipline. They can focus and occupy the same place as their horse, in a moving meditation.