I bought a cutting horse a year ago to be my new fox hunter --I immediately switched him to a snaffle. But like you I was concerned with the “stop and spin” that was possible with this very, very agile and athletic horse. What I did was add a “one rein stop” —be sure you have good instruction on how to train this --some think one just reaches down and yanks the head to the rider’s knee and the horse stops whatever he’s doing --no and if you do that, you might knock him off balance and both of you fall. Instead, starting at a walk, bring the head to you knee by reaching half way down the rein and pulling to your hip. When the feet stop moving (they will) and the horse relaxes the taught rein by “giving his head” immediately release the rein (and I mean IMMEDIATELY). If the horse starts moving off, do it again. After 100 times spread over 5 days (doing i both ways, each hand) at a walk, the horse learns when you slide your hand down the rein, he needs to stop because his head is going to be going to your foot. And he stops when he feels that forward slide down the rein. Then you do it at the trot --but that’s really easy because horse knows the drill. Ultimately, you practice (on good footing) cantering a few strides, then shutting horse down with a one-rein stop. Canter a few strides, one rein stop. After you have done that a month or so --you will do it instinctively. Any time you feel uncomfortable in the saddle, slide hand, wait for feet to stop moving. Release.
Does it work --YES --two weeks ago I was hunting my horse with a big group. As we came out of the woods, the horse ahead of us BUCKED TO THE MOON. My boy started to speed up (bolt) --I said out ;loud, “One rein stop,” and I did it and HE STOPPED RIGHT THERE. I was standing still while the field was flying away --and my horse never moved. He’d learned to respond to a one rein stop!!
I follow a set of DVDs that show a Western Rider teaching his horse “the basics” on the ground and mounted. For me, with no access to a trainer, it’s a lot of fun and my horse and I do about 30 min of DVD stuff every day. We have both improved --I understand him better (I’m an English rider) and he understands me better. I couldn’t understand the repeated emphasis on the one-rein top --until I needed it. Now I “get it.” If you want to know the DVD series I follow, PM me. Any time someone names a specific trainer on COTH --there’s a fire storm of “He’s Terrible” --so PM me --but honestly, all the DVD trainers, Western anyway, seem about the same. I just like how “mine” is set up.