Don't bother with the horseback ride unless you have a child who will be happy to just sit on a horse, or if you are not a real rider and would be thrilled to just be on a horse. The horses go nose-to-bumper at a crawl along a very dusty trail. The scenery is pretty, but you could see the same scenery in less time by taking a brisk walk (on your own feet.) This is not a "ride" where you are actually controlling your horse in any way. Also, it takes a very long time to load everyone onto their horse - it is done one at a time while the cowhands make a big deal about choosing the right horse for you. It was a full hour after the appointed start time before we rode off, and we covered a very, very small distance, never out of sight of the ranch. I really felt like we wasted the morning.
On the other hand, my daughter, who was 11 and loves horses but has never had a chance to ride except in these kinds of situations, was thrilled to pieces. She thought the cowhands really "matched" her to her horse. She thought she did a great job "steering" her horse, because it stayed in line and actually moved. (and really, under those criteria, she did, b/c some kids couldn't get their horse to move and had crying fits, and everyone had to come to a halt numerous times while a guide went back and got the horse to move.) She thought going under willow trees at the end was a big, risky thrill. And I loved watching her have fun.
So it totally depends on what you are looking for. If you have any experience on horseback at all, skip this and apply your money to the ATV ride. That really was thrilling, had great scenery, and had us all cackling with glee the whole tmie. We still talk about it a year later.
As for the shoes - if you'll do real hiking the day you're on your own at the GC, then it's worth it to carry the boots in your luggage and also wear them on the Arch hike. Or, if you have weak ankles, definitely do boots, b/c it's a lot of up and down. If you're steady on your pins, a good pair of trail runners, low hikers, or day hikers should be fine for you, and also comfortable enough to wear on other days. I wouldn't do the Keens, or other open-sided shoes on the Arch hike, because the sand is very hot and you could irritate your feet by exposing them to it. If you want more shoe detail, we on this board have been known to post pictures/links to our personal favorites (and it's an ongoing quest for many of us) and could probably be persuaded to do so again....