I have a QH that is an angel... so a few years ago tried to decide whether to breed her to a gaited stud, so as to get a gaited horse eventually. My idea was that I'd raise up the baby and have a replacement horse ready to ride by the time my QH mare was retired.
Well, I was advised that the odds were stacked against getting all the attributes I wanted - attitude, looks, conformation, gaitedness, etc. In fact, I had the same high odds of only getting all of the attributes I didn't want -- mismatched conformation, not gaited, or choppy gaits, clonky head from gaited horse bloodlines, etc. If you knew what types of babies the Friesian threw, and what their dams looked like, and also had an idea of what your mare produced when crossed with certain types of sires, you might have an guesstimate of what you could expect. In my mare's case, she was bred by different owners and always threw her pretty head and attitude, but the conformation and color and coat came from whatever stud she was bred to. It really depends on what type of QH bloodlines and sire prepotency you're working with. If that's what you want, I would suggest looking around and buying that cross - you get to pick sex, color, and make sure the combo of attributes is what you're looking for.