I am by no means an expert and I am working with the trainer at our barn, but I wanted to get some input on what I can work on with him on my own. I ride him in a loose ring french link snaffle that is fairly fat and he does great with it. He's very responsive when I ask him to turn and has a wonderfully soft mouth.
So here's what he does now. When I ask him to stop, I apply pressure straight back on the reins (pull them to my hips) and say "Ho." He knows the verbal cue well. I also sit back/down into the seat of the saddle (I ride in an Aussie saddle). He will pull his head in (luckily he doesn't throw it up!) as far as he can, but he'll just keep on walking. He doesn't exactly fight the bit, he just ignores it, really, until he decides to stop.
So, what can I do to stop him from pulling through the bit?
We had an issue today where he took off trotting (totally my fault...was trying to give him outside leg and accidentally gave him outside heel instead, so he took that to mean I wanted him to trot). Trying to stop him was like trying to stop a freight train...an incredibly smooth freight train, but a freight train nonetheless. I remembered one-rein stopping right before we reached the fence and started to pull him around, but I'm left-handed and so I naturally went to pull to the left, but the fence was there. By the time I went to switch sides, he had already stopped of his own accord next to the other horses in the arena with us. We kept on working for a while longer and he was doing well, but when I asked him to stop, about three-quarters of the time he would just ignore me for at least a half dozen strides, usually more.
Someone suggested one-rein stopping and or circling him until he stops. I did try a one-rein stop on him at one point (after our trotting incident), and he did stop, but he kind of jumped sideways a little like he was ticked off that I asked him to stop like that.