The Horn could very well be the same horn that appears on the Zamorakian standards.
-Ascertes, King of all the Hallowlands and the Everchosen of Saradomin.
So for the horn we have now even more possibilities-
1. It's the frostenhorn, now being used by the Zarosians to contact Zaros, retrieved from Ghorrock by the adventurer, its powers amplify basic power such as the small amounts of frost and demonic energy in ghorrock, amplifying it to the point where it created an ice demon, and froze most of the fortress over. Its power has been recognized by the *ahjarrat race, who proclaim that its true name is too terrible for human ears.
2. It's Quin's horn, used by the character mentioned in POP to control sea creatures and spread her rule throughout the Eastern lands, amplifying her already significant ability to control sea creatures to the point where she used to control a formidable army of strange creatures of the oceans and even expressed desires to be worshiped as a goddess, but was stopped thanks to the adventurer's help. now the horn's location is unknown, possibly acquired by another god or sorcerer.
3. It is the horn seen in Zamorak's icon, similar to how Saradomin uses the Star on his crown as an icon and Armadyl uses the symbol adorning his staff as his, it may be possible that Zamorak discovered the horn and used it possibly when Zaros was overthrown, but likely before the eruption of the god wars, when the symbol became known adorning those who ally themselves with the self proclaimed lord of chaos.
4. Possibly Guthix, seeing the horn and recognizing its potential to ascend a mortal to godhood and not wanting a mortal to corrupt his world in such a way, broke the horn in a similar manner as his sword, and parts of it may have become known separately as powerful power amplifiers (see 1 +2).
"We call it being a hero"
Yeah pretty much what you said but I disagree on the horns being anything to do with Zamorak. The reason this theory has came up is people stereotyping gods based on the actions of 2 of their number. Just like Guthix did.
by the staff of Armadyl, it means that it is an elder staff, that was in Armadyl's possession for a very long time, likely causing him to be able to ascend to godhood, and was used for most of the duration of his following's existance, due to the use of the symbol at the top of the staff to signify Armadyl's kingdom. Its like if you were given a house, that you lived in all you house, most would consider it your house, but technically it wasn't built by you.
I believe the staff is also much stronger than the elder crown due to Armadyl's seemingly faster Ascension, as from Guthix's memories we can see that Saradomin had the crown for eons, before Guthix even found runescape, but guthix found the staff on runescape, suggesting that somehow it came into Armadyl's possession sometime afterward meaning it would need to be stronger so Armadyl could match Saradomin's strength when they were both on Runescape.
"We call it being a hero"