I do not carry a horn, unless it is something like a dove shoot. A half dozen premeasured loads in pill bottles is usually more than enough. A horn is a good device for storing or moving a quantity of powder. More powder than a day's outing might want for.
Two or three hundred years ago powder was a necessity that you likely had to go a ways to procure. A horn was a good way to keep it safe and dry IN THE HOME. If you had a pound or two in the horn for storage I very much doubt you would want to bring it all along every time you set foot in the woods. Pretty sure the ancestors on a day trip carried the load un the gun and fixings for maybe 2 or 3 more shots. A muzzleloader is neither full nor semi automatic. Its technology imposes limits on how much shooting you will do.