I'll respectfully disagree with Calamity on the grazing issue. imo it's never a good thing to never allow a horse to graze while riding. I like the saying "Never say never, don't always say always, but usually say usually."
Letting a horse eat with a bit has never appealed to me because it's a piece of metal he's chomping and trying to chew grass with it in the way, aside from the grazing getting out of hand possible issue. I don't allow my horse to lay down with me for a roll either.
(said tongue in cheek!)
I'm on the horse's back, he's got 20 hours or so of the day to graze, he can hold off for the short time.
But you're right....to each their own. If that floats your boat, that's cool. But I can't say it's fine. I've got too many people asking me how to cure their horse's bad eating habit.
If the horse truly respects the rider, he will stop grazing when asked to with the slightest suggestion. My horse is highly motivated by food, he LOVES food! lol. But I still use this pattern of going to grazing spots if he is feeling a little lazy some days, and when I ask for his head up, he gives it right to me. No fight, nothing.
But that's just it. This horse doesn't respect the OP.
You have worked with your horse enough and you have enough experience to know how to handle it, and your horse respects your wishes.
I help people who don't have that from their horses for various reasons....they are just barely getting the basics of NH training and the leadership stuff and all that....so if they are learning themselves and having trouble on top of that....I can't tell them, well go ahead and let your horse graze....after I've put too much time into retraining the horse to listen to the rider and retraining the rider not to pull on the horse's mouth for any reason (that is a HARD lesson to teach).
Some people can't allow their horses to graze because the horse will tear the reins from their hands and will become so adament about it, they buck or totally ignore the rider, the rider goes to old habits of pulling on the horse's mouth....it's a mess.
So, I just tell people....don't do it. Your horse has all day to graze to eat to be a horse. When you're on his back, he can pay attention to you.....that's just easier.
But yeah, sure, if you've got full control of your horse...go ahead and let the horse graze....
BUT the OP is having enough trouble already with the horse, why add another possible issue? If the rider can't get the horse to move....who's to say going from grass spot to grass spot can be an invitation for a bad habit? At this early time of horse and rider getting to know each other....
I'm just anal about preventing problems, I guess.
NUTTY SADDLER: YES!!!
That's another way, too!
If you don't mind, I'd like to add a little to your idea:
Pick up the left rein (using a plain snaffle: full cheek or dee ring)....and bend the horse's head around to your stirrup. Bump your legs against his sides. WAIT. Hold. Wait.
The horse's neck will get tired and when it does, the horse will move his body. When he does, he will step to the side or forward with one front foot. When he does, let go of the rein and stop bumping. Repeat with the other rein.
If you do this way, you can "unlock" the horse's movement.