I just want to say I have four cutting bred horses- two show horses and two using horses and have owned others. The bloodlines here are Doc Quixote, Smart Chic Olena, Holidoc, Quejanaisalena, etc. My show horses are NCHA money earners and will certainly react to a cow, but are the steadiest, most dependable horses you can ask for. I pulled one out of the pasture on Sunday and took him for a trail ride and he had not been ridden since mid-November. He was an absolute angel and could not have been better behaved. The only lunge line I own is in my horse trailer for emergency loading situations and I am too lazy to round pen. I just get on and ride!
Any horse, regardless of bloodlines, can be reactive or quiet depending on training. I, for one, would buy cutting horse bloodlines anytime! And for the record, I no longer show- I only trail ride!