From the UESP:
Falmer, or Snow Elves, are a race of Mer (Elves) that lived on the continent of Tamriel.
The Falmer, like many elves, were proud people with a unusually high skill at magic. They had a strong resistance to frost as their skin was coated with a thin layer of blue-white ice. The type of dwellings they lived in is unknown. The only known weapon that they used is the spear of the Snow Prince, described in "Fall of the Snow Prince". It is rumored to be kept in the tomb of the snow prince littered with other treasures. The spear could simply absorb the life out of its opponents and transfer their energy to him, finishing the foe with a powerful frost blow. Many adventurers have attempted to find the tomb but none have prevailed. The Falmer were a energetic race but also a race that generally kept to themselves; hence little is known about them.
History
It is believed that the Falmer were the original elven inhabitants of Skyrim, the northernmost province of the continent, and were defeated and displaced by the Nords. The Pocket Guide to the Empire, Skyrim chapter mentions the Snow Elves as a local superstition, with Nord villagers blaming them for a number of random misfortunes and scant physical evidence of their existence.
Little is truly known about the Falmer. No cities have been found, and only one book remains (see below). They fought endlessly with Nords, since the latter were in their expansion campaigns. It was in this time that Nords and Dunmer were battling in Vvardenfell. The Falmer had a presence on Solstheim north of the island of Vvardenfell.
There exist four opposed hypotheses about the fate of the Falmer. The Skaal claim that the pesky Rieklings are, in fact, descended from the Falmer. Conversely, the Altmer in Raven Rock claim that the Rieklings are simply snow goblins, and that the Snow Elves have blended with the other elven races through interbreeding. The book Fall of the Snow Prince, found in a burial barrow, seemingly supports the second hypothesis, describing the fall of the Snow Prince, an elven leader who faced the Nords in the Battle of Moesring.
A third theory considers that there is also the possibility that genocide was committed upon the Falmer, and if so, likely by the Nords during aggressive wars for territory. A scholar who traveled to Solstheim (circa Nerevarine) in search of these elusive beings uncovered proof of their existence. He left for Skyrim, where he thought he might find more about this people.
Finally, it is theorized by some that the strange race known as Ice Warriors, found in the icy caves of Glacier Crawl may be the last remnants of the lost race of Falmer. These beings are uncommunicative with outsiders, but are icy blue skinned humanoids, with features somewhat between Elven and Orcish.
And from the Imperial Library you've got http://www.imperial-library.info/fsg/nazzarticle3.shtml debating the relations of Rieklings to the Falmer and http://www.imperial-library.info/mwbooks/bm_aevar.shtml.
From the Pocket Guide to the Empire:
Nords attribute almost any misfortune or disaster to the machinations of the Falmer, or Snow Elves, be it crop failure, missing sheep, or a traveler lost crossing a high pass. These mythical beings are popularly believed to be the descendants of the original Elven population, and are said to reside in the remote mountain fastnesses that cover most of Skyrim. However, there is no tangible evidence that this Elven community survives outside the imaginations of superstitious villagers.
Uncle, I saw signs that might be Falmer boundary-runes, but nothing sure.
If any survive, they are wary and withdrawn.
And the Elder Scrolls Treasury III:
According to ? Nord legend, the Falmer or 'Snow Elves' are an elusive race of Elves who dwell in cold, remote regions. Since they bred with the other Elven races, they ceased to exist as an identifiable culture. They're usually blamed for any number of disasters.
AND NOTHING IS CONFIRMED ABOUT TES V. We don't even know if there'll be one (although it's likely).