Sorry if i skipped through the thread, but just to OP. I believe that Falmer is the name given to devolved Snow Elves, not so much like Wood Elves being called Bosmer or Dark Elves Dunmer. But, then again the word "Mer" meaning the Elvish type races could mean you are right. Its kind of a swings and roundabouts thing that maybe the DLC will answer.
The one thing that stands out to me is the Y'ffre act the Bosmer participate in. This makes them into supernatural beings in desperate times, something they call the wild hunt. Problem is, they can not turn back to the normal Bosmer form and often become dangerous. Sometimes this is said to be where monsters all over Tamriel came from. Maybe just maybe the Snow elves had a similar ritual and attempted to use it against the Nords. But instead of it being offensive, as the Bosmer used against the Nords to kill their high king (this happened later I think?), maybe it backfired and they became beast like devolved creatures, and more territorial and subterrainian defensive creatures than the Bosmer Y'ffre creatures offensive nature.
Then again, all that doesnt answer whether or not Falmer refers to Snow elves or the devolved form they now exhibit.
No. The lore that I gave a link to is pretty specific that the Falmer is the Elvish word, and Snow Elf is the Nord translation of the Elvish.
You don't hear the Altmer calling themselves 'High Elves' or the Dunmer calling themselves 'Dark Elves', they simply call themselves 'Altmer' and 'Dunmer'. In the same way, the "Original" Snow Elves called themselves 'Falmer'. Just because there is a massive change to the race (in this case due to a highly poisonous, magical mushroom that the Dwemer forced the Falmer to eat once they betrayed them into slavery), doesn't mean that they're an entirely different species from the original. And it's very clear in the Lore that the Falmer changed in appearance due to what the Dwemer forced them to eat.
Also, the greatest modern reference that I can name that says that the Falmer and the Snow Elves are
still the same species is a reference made about them in the Thieves Guild quest line.
You are charged with getting the old Guildmasters' Journal translated. The Mage you take it to in Winterhold
says that the language it is written in is Falmer. The translation stone that Calcelmo keeps "safely" guarded is a "rosetta stone" for the Falmer language. Both dialogues/quest info reference that this info is thousands of years old. They reference them as Flamer and Snow Elves with the interchangeability of them being the same race/species of Mer. And this is
in game info that coincides with the Lore.
Falmer = Snow Elves and Snow Elves = Falmer.