I always ride with a rope halter under the bridle. Unless we are doing a parade or something, and then I will go sans halter. For me it is a safety issue, whether it be for tying, or extra control. Sometimes on trails I will eventually take his headstall off during the ride and ride with just the rope halter. As for how it looks under the bridle, alot of his tack is black, and his rope halter is plain black. I don't think it looks too shabby :)
I ride with a group of friends sometimes who are very opposed to riding with halters, and on one of our trail rides one of them had an incident where the headstall buckle broke and came completely off. We finally rigged it up MacGuyver style with someone's shoelace (my friend rode the rest of the trail in just her socks!). But this could have been an easier fix if they had a halter on the horse. Not to mention it was hard to get the horse stopped when the incident happened.
I do not believe in heavy clasps or anything hanging from the halter, I have a no clasp, knotted lightweight rope that ties onto my saddle. My gelding LOVES a good head rubbing on the tree or post he is tied to, so usually I tie him with the lead rope, and slip the headstall off for lunch breaks. Which is another advantage, IMO, because I do not want him scraping up his headstall and/or bit on whatever he decides to rub on.
Just my opinion :)
No hour of life is wasted that is spent in the saddle. ~Winston Churchill