I think it ultimately boils down to personal preference, but lot of old-timers carried the horn suspended from the strap of the shot pouch. This is an illustration by Kurz of Edwin Thomson Denig's rifle, pouch, and horn:
Denig was the
bourgeois at Fort Union in the days of the buffalo robe trade. It looks like the horn is attached with short straps with buckles, so its height could be adjusted independently of the pouch, or the horn could be easily removed. This pouch and horn from the Carolinas has a similar arrangement:
There was an article about Canadian powder horns in a back issue of
The Museum of the Fur Trade Quarterly which indicated carrying the horn and pouch on separate straps was generally practiced in Canada, but south of the Medicine Line you more frequently see the pouch and horn suspended from the same strap. That seems like a sweeping generalization, but I won't argue with it.
These are native shot pouches with horns attached, from San Ildefonso...
...and Taos:
This old pouch and horn rig, from the Cowan's auction site, must have seen a lot of use in its day. The strap is somewhat the worse for wear, but the horn is still attached to it:
Incidentally, that little doo-dad on the right, suspended from a string, is a small bar of lead. Any idea what that might be for? It must be there for some purpose.
Back to the original topic, I think it was pretty common for the horn to be affixed to the strap of the shot pouch on the American frontier, but I doubt it was universal. I usually carry the bag and horn on separate straps, but I wear both on the same (right) side. I like having access to both with my dominant and most dexterous hand. I have also found some potential for getting the strap fouled with the gun butt when shouldering the weapon, if there is a strap across the right shoulder, and I don't like having straps across both shoulders in any event. Too confining.
However, that's just me. Others are welcome do do as they please. By all means, experiment with your options if you are not sure, and figure out what works best for you.
Notchy Bob