I love the pirouette. My mare just started doing it at the trot, and was only doing a 1/4 turn at a time. I don't want to sour her at something. She is super athletic, and this comes easy to her.
I pirouette still has some forward motion, yet is in a very very tight circle. You always want that forward movement. If there is no forward movement, then you are doing a piaffe.