Depends on if you consider divergent evolution to be true and working in skyrim lore.
This^
Evolution. Snow elves were changed by their environment. Two actual snow elves remain: Gelebor and Vyrthur. The rest (the falmer) are a new species now, as they pass down traits the original snow elves did not have. They had adapted to a new environment. Finches of different species share more similarities than differences, but they are different species. Evolution. Now compare Gelebor (one of the last snow elves) to the falmer. Clearly related, but no longer the same species. Mutation, magic, whatever caused it - the DNA has changed, unless falmer offspring are like Gelebor/Vyrthur and then change into "falmer form" (which is not the case, AFAIK).
Also, looking at Mysterious One's post (above), and the OP's original post, I'm remiss not to remind: races are not the same as species. Humans (black, white, asian, latin, middle-eastern, etc) are all the same species - but different races. Just like dogs have breeds but they're still the same species. So, to reinforce, I feel that the falmer are a different
species than the snow elves, due to evolution and, after their initial creation, natural selection. I believe Gelebor himself says so.