I agree with deserthorsewoman. That arabian is also probably a stallion, therefore showing off more. I think if any horse had that much energy being kept back (since they were walking the horse in and then all of a sudden released the pressure) they would prance around a bit like that.
And where I live (Midwest) there seems to be quite a few Connemaras. I know of three purebreds. They were used at a children's lesson and therapeutic barn. I'm sure there have both several others there too that could have been part breed. They seem to be a quite favored pony for lessons.