Great pictures!!! I lovelovelove Buckskins!! =)
In the first picture of the bay horse, I don't know what is being asked of the horse, but either way, the rider, in my opinion, is pulling the reins way too high, and they don't have a firm enough grasp on the rein itself. If the horse popped his nose out, I think those reins would come right out of their hands! =)
Proper hand placement for western riding is even height with the horn... and for Eq. I think.. think.. the hand is supposed to be -next- to the horn.. and in pleasure its supposed to be just infront of the horn, but equal to it in height.
Pull the rein toward your hip, not your chest ^_^ You should keep enough slack to have control of the horse, but you shouldn't have consistant tension on the bit (unless its a Walker, lol!) I assume from the pictures that both riders were riding Western Pleasure, not Equitation because of the spare hand placement.
I also think the bay rider could stand to let about 1 more hole down from their stirrups.. I know in english the bottom of the iron is supposed to tap your ankle bone (at least that's how I learned it for flat work, AP). In western, I forget.. LOL I just adjust my students stirrups until it looks right. Your supposed to have a good feel of the stirrups, but not have a scrunched knee. Google some Western Pleasure pictures to get a good cross reference of examples :p
The knot in the reins in the last picture with the Buckskin also seems to have the reins pinned too short especially considering that's a *counts the stride* ... lope? Its not a walk or a trot.. unless he is gaited, lol! And again, the headcarriage seems a hair on the high side.
But the good news!!!
In that second picture with the Buckskin he looks SUPER flexible! I bet he neckreins like a dream. It looks like you just gently lay that rein on and he instantly changes direction. Marvelous! I love a supple responsive horse!!
And I think the first picture is awesome. Nice long relaxed rein (so many people keep tight reins even when standing still.. control freaks!! LOL!) and the horse looks relaxed too. Everyone is having a good time! My horses were always batty at horse shows.. yelling at the other horses, bucking, being mean, etc. I wish I had a laid back show horse! LOL! The sad thing is, the bulk of the time I was showing western on these "wildfire" horses LOL!
All in all, good pictures! I tend to critique horses more than riders, so forgive me if I mis-pinned something =/ I've been focusing on training and green breaking more than riding instruction in recent months, lol! I swear im just no help lately! LOL!