So in my opinion greybeards are odd-monks-sitting-on-mountain-talking-to-sky guys. But there is something strange about them and that damn place, High Hrothgar.
So this mod adds 5 new dragonpriest masks:
The Wulfgar mask
The Borri mask
The Einarth mask
The Arngeir
The Jurgen The Liar's mask
So let's start the lore thing:
MAYBE the greybeards are secretly dragonpriests like their ancestor - Jurgen The Stormcaller. If you think about it, that some monks on big mountain worshipping the dragon language it's weird
ATTENTION!!!
I HIGHLY RECOMMEND TO ONLY USE DOORS THAT WILL TAKE YOU TO BASEMENT AND BACK! THERE IS A DOOR TO ANOTHER LOCATION SO DON'T WALK THERE, I WARNED YOU!

My other mods:
Vanilla Dragonpriests followers at Skyrim Nexus - mods and community
Elder Scrolls Online Dragon Priest Followers at Skyrim Nexus - mods and community
Dragonborn Dragonpriests Followers at Skyrim Nexus - mods and community
The Ultimate Dragon Priests Followers at Skyrim Nexus - mods and community
The Hoplites at Skyrim Nexus - mods and community
 Spoiler Journal (DON'T READ IT FOR OWN EXPIERENCE!):
As you climbing to High Hrothgar this time, you notice the skeleton. It have Ulfrics mask (former student). After that you found Vynsillus Tatrovon's journal about greybeards worshipping dragons and Jurgen 'The Liar'. And after you read it, you see door. Door that you have never noticed. Inside it there is lich Jurgen The Liar. After you defeated him, you took his powerful mask and robes. But then you see strange shrine with masks. You can recognize initials of every single greybeard: Borri, Einarth, Wulfgar and Arngeir.
In basic language to find the door, you need to find skeleton of Vynsillus Tatrovon and Ulfrics mask with his journal. In the place itself there will be Jurgen (very powerfull boss though with robes and mask) and masks.