JDI, the term Horsenality is something new from Parelli. Like people have personalities, horses have horsenalities and you can basically divide them into 4 main areas: Right Brained Extrovert, Right Brained Introvert, Left Brained Extrovert and Left Brained Introvert. Each horsenality has a different set of tactics you can use to calm them down, motivate them, get more obedience, etc. Right brain is the term we use for a fearful horse and left brain is the term we use for a confident horse.
But here is where an imitater and an imulator are seperated.......you have to know which strategies to use on your horse at any given moment and be correct. If your horse is right brained extroverted (running around, obviously scared) and you use a left brained introvert strategy........oh boy, you won't get anywhere!
There is a bunch of information on horsenalities on the parelli website.