Thanks, all! You got me watching videos on YouTube and wow, what I didn't know I didn't know about cutting!
See, my only experience with cutting was once many, many years ago. I'd finished my ride (in the arena, English tack) and was watching the boys (not real cowboys) "help" the rancher move a herd from one field to another. I stood a ways back from the path they followed, most of the herd in front, and while I was enjoying the beautiful scenery and weather, my QH was watching the cows. Suddenly I was airborne and it was only by a lucky grab of mane that I stayed in the saddle, because a calf had darted out from the herd, wanting to head back to the stragglers, and my horse "cut" him off, and got the calf back where he belonged. So without thinking about it, from then on I've believed cutting was natural to some horses, not something you taught, and that you needed cattle just so they could learn to read them, so to speak.
So how could a horse learn to work cattle by following a diaper? Ha ha! Not that I'm going to be cutting, that's a really difficult sport! I think I'll work to get my horse sharper on her responses, since we'll just be doing sorting, and if I can avoid embarrassing myself, and disappointing my partners, I'll be happy.
(But I'm still hoping my horse will learn this game herself, so I can just go along for the ride!