In the second video, she did not hold onto her reins for "control" of the horse when mounting. I'm guessing that you should hold onto the reins to exhibit you would have control of your horse while mounting? I would count against her for doing that even if it weren't against the rules. Even if your horse is broke, IMHO, it's just bad horsemanship to not have a hand on the reins when you're mounting. After all, you can never 100% trust a horse, no matter how broke, and to be completely without some level of control (even if they don't believe it's needed) is a bad choice IMHO. Have I done it? Yep, but it's not something that I would do in a competition.
Neither of them ground tied their horse to pick up a hind foot. Does that matter at all for scoring purposes whether you ground tie or just leave the reins around the horse's neck? What would you prefer to see? To me, ground tying just means that the horse will stand still while you walk away, regardless of whether there is a rein on the ground or not. I normally drop a rein just because I ride the traditional way with both rein tails on the left. It's easier to just drop one than it is to cross it over the neck. However, if I'm riding with the reins crossed over, then it's easier to leave them on the neck.
In the first video, I noticed he has his reins crossed and on either side of the horse, rather than your traditional "showing" rein posture of having both reins ends fall on one side according to the hand you are holding the reins with. He also switched to two hands to cross the bridge in a shanked bit, and then back to one hand. Again, I am just going to assume normal showing rules apply and you should do things one-handed with the reins on one side of the horse. On that first horse, I would guess that the horse is still relatively green, judging by the way he handles and rides (and if he's not......wow). That would explain the rider riding with the reins crossed over and using 2 reins for the bridge crossing, even in a curb bit. I would probably count against him for using 2 hands because it shows that his horse is lacking training. As far as having the reins crossed over or on the same side, IMHO, that's a personal preference.
I noticed that both of them had to switch hands in order to do the various obstacles that were required. However, would it be proper to move your rein ends from side-to-side when you switch (like normal "showing" rules) or does it not matter for ranch horse? This is where I would be unsure of the rules, but common sense says to me that it's fine to leave the tails on the same side, even when you are switching hands. Ranch horses are normally ridden with a left hand and any time a rider switches to the right, it's normally just for a short time and then they switch back to the left. I don't bother with switching the tails when I ride, I always have them on the left.
I know, I know, these are nit-picky questions. But I'm a detailed-orientated person and I like to do things right if I can find out the proper way to do things ahead of time.
I'm super excited for Sunday! If I can find someone to take pictures or video for me, I will .