Very nice horse and seems to be very quiet.
After starting horses for decades, I would suggest you do a little more handling on the ground to teach her to respond to your reins without resistance, as she shows there.
That won’t take five minutes here and there, where she learns to give to the slightest little pull, so you don’t have to pull at all once on her.
We call that installing a response of her legs to our asking thru the reins, for the horse to realize a little touch of the reins means to unpark itself and move legs and body one or another way.
Never pull on a horse, horses can hold and pull back much more than we can.
You already do that very well here and there when she gets stuck, but it is much easier if you don’t even have to go there, have the “unstick your feet” already firmly trained on the ground before getting on.
That halter is about two inches too high and too loose to be effective on a horse that doesn’t yet know to respond to your hand.
Would be more effective if set where the horse’s head is guided as you want, even better if those responses were practiced before getting on the first time.
Looks that you did a great job of desensitizing her so there were no fireworks with a rider on her back, that part was stellar.
She is cool with the whole thing, just seems a bit confused on the guiding, that I myself like to have installed before getting on.
A person on the ground helping move the horse on is a great way to go, if it is effective about reading the horse and rider and complementing both.
You did have that there, sure makes teaching easier when what we ask is made the easiest and smoothest for the horse we can make it.
One advantage, that helps those first few riders with forward motion, without the rider needing to push the horse forward, maybe causing a little resistance and tail switching if needing to be too insisting with our leg.
We don’t want to teach what we don’t want the horse to learn.
Hope that came across right, it is not a criticism, it is experience of years and colt starting speaking, hopefully helping your next rides and whoever else is learning from your video.
Thank you for posting it, the horse looks wonderful there, good job on that first ride being so uneventful, the horse not acting up.
To be able to starts colts uneventfully, like watching paint dry we say here, is considered one mark of good horsemanship.