Honestly speaking from experience (been riding since i was 3) if its a horse i cant trust on the trail we dont go on the trail, we stay in riding rings, arenas, exc. If I cant trust my horse to switch from bridle to halter we simply dont go, thats such a basic task for a horse. I have had horses who get a bit spooky (my TB mare) and even she was fine, if for some reason she tried to take off while switching I would use the reins around her neck, lead rope or halter which ever i grab first and keep her near me. I have even had horses who were so good about it i didnt even need to use something around their neck, my TB stallion for instance, he was such a gentleman after about a year under saddle, he was bomb proof and let you do anything to him... I think every horse is different as is the rider, if you cant communicate with your horse because of a halter in the way then thats not safe either. I always thought it was an awful mess under the bridle and 90% of the time there is a risk of one getting tangled with the other if you dont have the halter clipped up high enough, ive seen ALOT of riders who have huge halters on their horses and the halter is practically sitting on top of the bit. That to me isnt a risk worth taking. On the other hand I have always done alot of natural horsemanship and with that method of riding/training you shouldnt be relying 100% on your bridle anyway, it should be your body, heels, lower legs, exc.. and especially light hands, as i posted earlier i often ride in rope halters (with pressure point knots) savvy strings (just a string around their neck) and O or D ring snaffles. Honestly, I cant even remember the last time I rode with a halter and lead rope even with me much less on my horse. If we trailer somewhere thats different obviously, the halter is left with the trailer and only used during transport.
There was a time when I barrel raced and I rode with much more harsh equipment... i wont do that again though knowing what i know now about riding.