My family owns a small antique horn, probably from the Appalachians, that is finished pretty rough and except that it has no tacks looks very much like Muskrat Mike's example above - it was scraped smooth to the touch but not enough to eliminate the rasp marks that cover it nor the cut marks from the knife used to shape the tip. It is rippled from the scraper, too. However, it was thinned down considerably - not much more than 1/16" thick around the spout hole or the majority of the body (beetle holes allow me to see the thickness in the center), and thinning down to 1/32 or a hair less at the base. Tapered spout hole, too, incidentally. It is a pretty good example of a horn that had a good bit of thoughtful work to make it functional but little effort towards aesthetics (though, the tip is cut cock-eyed to the centerline of the horn in such a way as to accentuate the twist, and I wonder if that was done intentionally....)
The downside to leaving horn with the bark on is going to be really thick walls, no rings or raised to to keep your strap on (guess you could use a incised groove), and a thick, perhaps very thick, spout area, which will make pouring powder into a measure without spilling rather difficult. Might look interesting, but I doubt you will be happy with how it works.