I don't really think that the halter really gets in the way *much*. For the most part the onlytime i've ever seen anyone riding with a halter under the bridle its been in two situations. On trail, and typically then its with western types. With neck reining I don't believe that the halter will get in the way at all.

The other way i've seen it is when you are training young/unbroke horses. At that stage of the game you aren't really using the bridle for much of anything anyway. Its a safety thing so you have something you can lead them with while someone is on their back. They can *feel* the bit, but not be tugged on by it. I don't think its dangerous at all. Obviously once a horse is at a high enough level such practices do not really need to be followed.

I think that keeping a halter on under the bridle is something to be done if the rider wants that added security. My new mare is *very* green...she knows walk/trot and I feel completely comfortable riding without a halter under the bridle, but I'm sure some people working with her might not be comfortable with that. She has gotten a LOT better, but she is very spooky and untrusting.

Overall I think its more of a western/trail thing, than it is an english thing. That being said I ride Dressage, and my instructor will start her horses with the halters underneath. To each their own for the most part.