In one of the quests in Skyrim, you have to get some Phial and the guy who gives you the quest tells you it was created by infusing it with the magical snow that first fell on High Hrothgar! Can it be that the snow is the stone? I don't know... just calling it 'magical snow' made me think about it
Will the day when the sun would shine, hotter than ever and that fire storms would cover the whole of Tamriel the day when the snow on High Hrothgar melt and leave the tower without a stone? O:
EDIT:
Now that I'm thinking about it.... not really