Try going into a Kimberwick for awhile, and then switch back to the snaffle. The horse I have now was in a tomb thumb before I got him, and when I put him in a snaffle he wanted to run through it. I put in him in the Kimberwick for a few days and worked on seat aids. Then we went back to the snaffle and he was much better.
Also, before asking the green horse I'm riding to whoa I get her puffing a bit first. This way she wants to stop when I say it, then she gets a short break standing still then its back off at the trot/canter for a side or two then woah and break time. They start looking forward to you asking. I know its useless to ask the mare to stop soley off my seat and voice until she has let off the extra steam. Good time to prefect transitions too ;) Posted via Mobile Device