Okay, mages die, especially at lower levels, and mostly from not playing them as Mages. They lose the damage race to Warriors, every time, so the trick is avoiding that at all costs. You have to invest in Magicka, so you don't have enough health to take many hits even with Dragonhide.
A Mage is just not a Damage dealer, that's not how you win. Wizards use Effects, largely instead of direct Damage. TThe perfect example is Illusion with Conjuration, or Necromancy. Fury cannot win the fight by itself, because there's always that last man standing, but you can finish him with an Atronach, or his buddies that come back at full health when you raise them. Otherwise, stay out of the fight, you aren't a fighter, so leave it to those who make it their business.
The other option is any one of the Lore supported Hybrids like a
Battlemage,
Spellsword,
Sorcerer, or Nightblade. Especially when you're coming to Magic from Stealth, or playing Warriors, you can learn the startegies with the fallback of Armor, or from the safety of Invisibility. At least a Sorcerer has some Armor to make up for a low Health pool, Ebonyflesh is nice with Magearmor, but hen it wears off in an extended battle, you instantly go back to being a Glass Cannon. Real Ebony just doesn't do that. I usually wear Ebony Boots, and Gloves with Robes for Magicka assistance, and one of the dragon priest Masks for a Helmet. Specifically, Nahkriin, Vokun, or Otar are excellent choices. If you don't care about Matched Set, you can also wear Morokei with a heavy Curaiss (Like the Ebony Mail) for adequate toughness, and Magicka assistance.
This is generally the best way to learn the tactics, and techniques of a Wizard without being distracted by the inherent squishyness of investing in Magicka over Health with no real Armor.