I leave mine on most of the time (though i'll admit it's out of pure lazyness most of the time lol).
It's handy if you have to get off & lead or tie the horse. You can also use the lead rope on certain horses with your rein to help with turning/stopping.
I also like it when I have a horse (like my new mare) who is still learning to accept the whole bridling thing.
For me it's an OCD thing, I can't stand the cluttered look of a halter and a bridle together, LOL! So I never ride with both, unless we trailer away from home to ride and I don't want to risk taking a halter off to put a bridle on, or vice versa.
My horse lunged into the lake and the chin strap broke. I couldn't steer him and we were heading straight across the lake. I had a halter and a lead and could get the horse turned around. It literally saved my life. I can't swim and I am sure I would have panicked the further out we had gone.
I NEVER leave my halter on when I ride. Sometimes it would be handy but I hate to look like a sheepherder. I have a pair of hobbles that I can carry on my saddle if I think I might need to stop or I always have a lariet that I can use to tie my horse up if I have to.
I have my vanities when it comes to my gear and my horses. When you ride with REAL cowboys you learn very quickly that if you want to be taken seriously you must walk the walk and talk the talk but also look the look so to speak. I am quilty of not taking someone seriously as a cowboy if they have nylon headstalls, plastic saddles or halter-bridle combos.
When we go for a longer ride, we'll have a rope halter on under the bridle and have a lead rope on the saddle but not hooked to the halter. If for some reason the horse puts its head down or the rope comes undone from the saddle, the horse could step on or over it and cause a wreck. We leave the rope halter on so if we stop for a break, we can tie the horse up easier. A rope halter is light and doesn't interfere with the bridle.
If you were to tie with your lariet would you fashion a rope halter? Or rope around the neck? Just curious.
I personally ride with a rope halter under the bridle, but that's ok because there aren't any real cowboys around here for hundreds of miles! :)