I used to ride Red all the time with his halter on under his bridle. It isn't as pretty as without but it is practical.
I purchased a Taylored Tack Halter/Bridle for endurance riding. (hahahah not going to be competing for awhile though) While halter/bridles aren't as pretty as just a bridle - the practical side wins out - they are fantastic on a trail ride. In a second I can unsnap the reins and snap it to the halter ring like I did yesterday while I dismounted and handed The Biscuit off to my riding buddy while I trotted over to check out a gate opening. I can drop the bit set off of this halter bridle with one little movement. I love it.
I have a fairly new leather bridle that hasn't been on Biscuit since Christmas. I don't know that I will ever ride with it again - love the halter bridles!