FUR Armor??

[legoless]

What would Tamriel of the 4th Era look like if the Dwemer were still around and manufacturing this stuff and existing as a race?

It would be long destroyed.

Why do you say that?

The Dwemer did some seriously messed up things to the metaphysics of the Aurbis and ultimately destroyed themselves as a race. If the Numidium hadn't destroyed the world, no doubt some other mad invention would have, such as an early Celestial crisis turning Tamriel to primeval jungle. The gods they abandoned would have to intervene; there's no scenario in which I see both the Dwemer and the Mundus surviving into a Fourth Era together.

All of that has very little to do with fur armor though.

[The SheoDovah]

Or Sheogorath would have gotten offended at how boring(in his view) they are and inflict mass madness on them, throw an entire mountain range at them and drive them to the point where they end up destroying each other just for [&@%!] and giggles.

As for fur, it's kinda a fantasy cliché. Fur in TES is a really bad idea in reality. I mean, mages + fur = Burning to death but it looks practical in Skyrim and well, i'm not afraid to admit, I like the idea of fur bikinis. But for realisim, TES has done a lot worse. Such as fresh food in thousands of years old ruins. Single lockpicks in a wooden chest that hasn't rotted away etc..