#snaffle

first off, I would take the Argentine “snaffle” off ASAP, no offense intended, but those things are from the devil himself. (If you’d like me to go in depth about shanked “snaffles” PM me or send another ask.)

another important note is to make sure he’s not experiencing pain. get him checked out by a vet if you’re questioning his soundness. make sure all your equipment fits well. if a horse is in pain they will have a harder time responding to cues as they are simply trying to evade the discomfort. 

next, you’re not going to fix a stop by what you put in his mouth/over his nose unless the bit was causing severe discomfort that he was trying to evade. instead, it’s likely a lapse in training or bad riding (again, no offense) so I’d suggest going back to the basics, using lots of positive reinforcement to establish a good “woah”.

as far as equipment goes, its very dependent on his mouth conformation and your hands. my top three suggestions would be as follows:

french link/lozenge snaffle

the bit pictured has a nice mouth conforming curve, the link in the center keeps it from having the nutcracker effect. overall a pretty comfy bit if your horse is okay with tongue pressure. I have a lot of experience with it and find it works well.

low port

I used the bit above a LOT over the summer for flower, it worked really well for her since she hates tongue pressure, we also developed a really nice stop in it but that was more due to my seat than what was in her mouth.

ports are good for horses that have larger tongues (gives them room) or simply don’t like tongue pressure. I would caution you to be aware of the shape of the port, stay away from very square or rounded as they can cause jabbing of the tongue and roof of the mouth or suck up the tongue.

bosal (traditional hackamore) 

the bosal is really great if you need to get out of a horse’s mouth (has trouble accepting the bit, teeth issues, can’t find one that fits, need to try something new) or just want to follow in the traditional vaquero style. I love riding in a bosal, I’ve found that most horses have a really good feel for them. I currently ride my little dun mare in a 5/8″ rawhide core and my black mare in a 3/16″ roohide bosalita.

(I know a lot of other people on here would recommend a rubber mullen mouth, but I’ve never used one so I couldn’t say.)