So, it's never really stated in the College of Winterhold quest line what the Eye of Magnus really is - only what it may be - and so I wish to propose my own theory on it's possible nature.
We know that the Aldmer all built Towers in an attempt to copy the Ur-Tower;and, we also know that each Tower has it's own purpose (eg. Red Mountain and the Heart of Lorkhan allowed the Mundus to exist without the divine being there. Mundus was given a special divinity of its own). Now, the purpose and the Stone of Snow-throat is not known, however we do know it was somehow built by the Elves - assumedly the Falmer given that that is the region from which they hail.

Now, suppose that the Falmer built Snow-Throat, and the Eye of Magnus is the stone - the idea of this being the stone is plausible because the Nu-Mantia Intercept states that all the Stones are magical and physical attempts to copy the Zero Stone and they allow a tower to focus its energy to mold creation, and Ancano says that the Eye has the power to destroy the world (mold creation).

Go back to the arrival on Tamriel of the first humans from Altmora, and the idea is still important and connected to everything that occurred. I state it is still of import because I propose that the first settlers took the Eye and brought it to Saarthal, where it was kept until the Night of Tears. What followed is that perhaps the Elves struggled to move it after that and then, ultimately, failed to retrieve it when Ysgramor returned with the Five Hundred, after which Ysgramor perhaps thought it safer to just keep the eye buried with the city. The idea of this is perhaps given credence by this quote from 'The Fall of Saarthal': 'I can say with certainty that the initial attack on Saarthal seems to have been very focused, and does not appear to correlate to any locations that have been established as points of defense or importance. While the eminent scholar Sentius has yet to examine my findings, or indeed show any interest in them, my inclination is to suggest that not only did the elves know the apparent layout of the city, but that their assault was based on a specific directive and perhaps a singular goal'. Here, 'The Fall of Saarthal' clearly tells us that there was a specific goal behind the attack - and I propose that was an attempt to secure the Eye.

Another point of note is that the Nu-mantia Intercept tells us that Snow Throat is a mountain, and its apex is only half there, which - as suggested by TIL - may be because '[perhaps it exists in multiple dimensions]' OR, perhaps it's apex is only half there because the Tower is currently separated from it's Stone, though only physically, which ,at the time of the writing of the Nu-Mantia Intercept, resided in Saarthal.

And that is that! Those were my - probably flawed - ruminations on Snow-Throat and the Eye of Magnus. Criticism? ^_^