Howdy, Lanci, and welcome to the forum
Most of a horse's cow savvy comes from their bloodlines and is about as natural to them as breathing. A non-cow bred horse can be taught to be a little bit cowy, but no matter how well trained they are, they will never have the natural feel for the cow like a horse bred for it.
Perfect example is my Mustang Dobe. He has zero natural cow savvy, but has been taught
to work cattle and does a decent job of cutting. He's not great because he doesn't have the speed or agility really needed to be great, but he tries his heart out and wants to get it right. It took about a year of hard work to get him to this point and he will never be one that I can drop my hand on and just let him work. I always need to give him a pointer here and there.
He will never be able to compare to my brother's cutting bred horse. Snuffy is from good cutting lines on both sire's and dam's side and he was cutting cattle by the time he had 3 rides on him. In less than 60 days, brother could drop his hand and Snuffy would work a cow until you told him to stop.