If your powder horn is airtight, and it should be, powder can be stored in it indefinitely. Black powder doesn't really have an expiration date, but it can get spoiled by moisture or other contaminants.
Horn is really an ideal material for a powder container. It is waterproof and dimensionally stable, non-sparking, and it doesn't "sweat" like metal does with rapid changes in temperature. Horn is susceptible to insect damage, but in my experience, horns with black powder in them seem less attractive to bugs. I think the sulphur in the powder must repel them, to some extent.
Flasks are another matter. They do sweat with rapid temperature change, and I don't think flasks with valved tops can be made really airtight. However, if a metal flask with powder in it is stored in a climate-controlled environment, the powder ought to keep for quite a while. I have a couple of flasks and normally don't empty them out after shooting, but I do store the flasks in airtight containers. A ziplock bag works, especially if you keep a desiccant pouch in it.
I think you should be able to keep some powder in your horn. I think it was customary for old-timers to keep a rifle, pouch, and horn hanging over the cabin door, ready to go, so they could grab everything they needed in a hurry.
And, of course, old Rover was stationed under the front porch, so he could be right at the master's heel as they lit out for the woods...
Notchy Bob