I love the way it looks on my Nord chick. Despite being the weakest, it's arguably one of the best looking armours in the game. Is it possible to improve it to legendary? or is there a limit?

There is no limit. It might be a bit more difficult since it is Fur, but it's possible with a combination of Alchemy and Enchanting.

Since Fur has no material perk associated with it, the best you can get it without smithing buffs is "Flawless" at 100 skill.

You can get it to "Legendary" if you can get your effective skill up to 168 (for example, 100 skill + 68% boost from potions and/or enchantments or some other combination).