I ride both ways. To be honest I can't tell much of a difference. We have two horses that I ride regularly and usually ride with the halter under the bridle. One, so I can tie them up when out on the trail, two for safety, and three because I'm lazyI keep the lead rope attached to the halter and hung around the horn, that way I can grab that on my way down, or as the horse runs past me (which has happened several times).
However, I ride western only and both of our horses neck rein very well. Our bridles don't go over the nose so that would also cut down on pressure/tightening.
So you have an idea of what I'm talking about. I also use rope halters. You can see the lead rope swinging on her left side, I'm not sure why I tie it on that side other than it always seemed to be the side she dumped me on, or ran past me after she dumped me. Our riding horses were both extrememly green broke when we got them. If you noticed, I ride a gag bit with my girl, and my sister's horse with a tom thumb. Both Leverage Bits.
I use a harsh bit because she is so high strung and spirited. I recently found out my mare was MOST DEFINITELY a retired barrel horse. I took her to my first horse show ever and competted in barrels, our second time running barrels EVER, and my 21-year-old mare came in 3 seconds behind the winner!
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