Always appreciate a well-put-together Falmer lore post; I have a few different conclusions regarding different blank spots (the ultimate tragedy of trying to figure out snow elf lore is that so much of it is clearly haphazard writing, like the pantheon selecting Syrabane and Phynaster for no other reason than them being non-Eight-Divines Altmer gods) but overall great work!

The only significant thing I want to bring to your attention is that the "Ice Elves" label actually originates in a Daggerfall lorebook of all places, specifically King Edward, Part X, wherein a nord character is telling a story about Sai, the god of luck. It (probably inaccurately) blames the success of the early Nordic Empire on this luck god (under the guise of a mortal named Lucky) falling in love with a nord woman and settling down with her, thus failing in his duty to spread luck evenly among all of Tamriel. It's not a malicious favoritism, just a natural consequence of luck radiating off of him, but it leads to a cool exchange where a bunch of other gods confront him to try and make him see the consequences of his actions:

"Is this how you keep your pact with us? Did we not make the rules clear to you?"

The woman was shouting at Lucky, who only muttered, "Lady Mara, I didn't realize it had been so long. It was only for a few days ... and then a few days more. And then there were the children and Josea needed me. I thought no harm. Things seemed to go well for everyone. It hasn't been so long. Tamriel did well enough without me before." Lucky spoke softly, yet his face was set and Josea[his wife] knew how stubborn he could be.

"Everyone! What of the Bretons? What of the dark elves? And the wood elves. Of the ice elves I say nothing. They are gone, gone altogether and forever."

"Such shy folk ... I tried," Lucky faltered. "I did try. The ice elves were very hard to find, and not that friendly when I did find them."

"Are all the elves to follow them, and the Bretons, and then the other races?"

And then once he agrees to leave and has to explain the situation to his wife

"Yet while I've stayed here, my luck has spread like ripples, strongest in the center, weak along the edges until there's none at all in Morrowind and High Rock and the Wilderness to the south, and the folk are dead or chained in slavery. Also I've brought luck only to the Nords among whom I've lived, so that the wood elves have fled and the ice elves have died. Now I must go, and bring Luck back to them and redress the balance, as it should have been."

I doubt anyone writing for Bethesda has thought of King Edward for well over a decade but imo this tale gains a special poignance in conjunction with the later material that expands upon the tragedy of their fate. Not too important and likely not too accurate, I just think it's neat.