First of all, I know next to nothing about powder horns, although I've made a few for my flintlocks. You might look over this website for better/more accurate information-->
https://americanlongrifles.com
After looking at your pictures I'd be inclined to say that it is an original horn, but from what period, I can't say.
It looks to me like the maker either used a file or rasp to take the horn down and then used a scraper to finish it. I would think if someone made it in more modern times, they would have used sandpaper to finish it. The use of a rasp and scraper back in the day would have been appropriate. Also, how they cut the spout tip off looks like the used a rasp to even the cut up, rather than a smooth finish that I think someone who was making a reproduction horn would do. On the other end of the horn, what did they use to pin the wooden end to the horn? Wooden pegs would have been appropriate, and the wood itself looks like it has a good amount of age to it. The holes in the horn where the wood gets pinned in looks like they were countersunk by using something like a knife, rather than a drill, and perhaps the pins and wooden end are later additions/replacement to the horn. There's also some type of checkering, for wont of a better term, around this end of the horn which leads me to believe the wood and pins are not original.
So again, I think there's a very good chance the horn is original, or if it was made in more modern times, the person making it knew how they were made back in the day. But as I said, I know very little about horn styles, how to date them, etc.
What's the information you have on the horn.