Your question is a good one. It obviously depends on what kind of stopper you are going to use in the horn, and how big a hole you want. The larger holes make it easier to get the powder in and out!
You can buy a tapered peg reamer at the hardward store to use to make a beveled hole for a violin peg, if you want to go that fancy. Just match the diameter of the hole to the peg or plug you want to use and ignore that advice.
I have a priming horn that has a very small hole, and a standard sized powder horn with a peg stopper that is probably somewhere between 1/8 and 1/4 " in diameter. I certainly have seen larger holes in other horns. Very large horns were often used to carry grains, and even lard, and salt. So, don't take literally everything you see in an old horn in a museum as representing the condition of horns used for gunpowder. I suspect that a hole of 1/4" to 3/8" might be appropriate for a horn used to load a musket, but by the time you get to the 1770's, you see premade paper cartridges supplied to troops in a box, and powder horns no longer are used in military ranks for the regular footsoldiers. That is one of the differences between the British soldiers and the Colonial forces in our Revolution. Washington would have preferred to supply his men with muskets and patched balls, but until France finally became our Ally, that could not happen. The early fights were done by men mostly using powder horns. Certainly the settlers that lived west of the Alleghenies used powder horns when fighting off the Indian raids.
