I would like to see a system in skyrim that makes different armors more suitable for different things.

Sneaking: this is my primary concern. Sneaking in lets say leather armor should be easier to sneak in than sneaking in chainmail or a shiny plate armor. If you stand in a dark corner, the dark color in the leather shouldnt give away your position as easy as if you were hiding with a shiny chainmail.

Movement/Actions:

Heavy; Heavy armor should decrease your ability to make fast and swift attacks, heavy armor should make your character feel more clunky and focus more on raw power than fast, agile attacks. It should really feel like you're this badass dude in the heavy armor swinging your two handed axe to kill. You are the hulk, not the flash.

Medium; Medium armors should be like a mix of heavy and light armor. A hybrid.

Light; Light armors should make your character feel more agile, more swift and faster in general. Wearing light armor makes your movements more fluid and quicker. Instead of swinging the badass 2 handed axe, maybe you are using two short blades do deal more spike damage than burst.

I hope you see my point, armors shouldnt only give your character armor, it should affect other things aswell and I've given you a few examples on what I think is a good idea

About Light, Medium and Heavy Armor:

I reckon they should ditch all the armor skills and just replace it with one, STRENGTH; the higher your strength the heavier armor and weapons you can equip. Using slow heavy weapons increases your strength more than using light weapons.

So an axe using character will quickly level up strength and be able to use the heaviest (heavy) armor.
A bow/short sword using will moderatley level up strength and would be slow and restricted in the heaviest armor so should use lighter armor.
A mage would be better off using enchanted clothing.

And your stealth should be inverse to the weight of your clothing, so heavy armor makes a lot of noise and no clothes makes no noise (you would still be able to be seen though).

In general the heavier armor you wear, the more noise you would make, but each armor can have a defined noise level to them and that could affect stealth.

Or in fact depending on the encumbrance and the coloring of the armor, each armor and clothing can have a stealth factor attacked to it that would affect the effectiveness of the stealth of the one who wears it.