Use measures to increase your magic resistance or just frost element damage. (Answered in another Gaming SE question here: What should I do to mitigate heavy spell damage? )
The reason you might find frost-breathing dragons hard, but not fire-breathing ones is that because your character, a Dunmer, already has constant 50% resistance to fire.
Get a follower that will tank damage for you, preferably a Nord (Nords have 50% resistance to frost).
Frost dragons are weak to fire. Since you mention that you are a Dunmer mage, specializing in destruction, then hit that dragon up with Fire spells. List of Fire spells, staffs and weapons here: http://uesp.net/wiki/Skyrim:Fire_Damage
Take the Impact perk, as soon as you can. This will stagger dragons if you hit it with a spell casted with two hands (temporarily stopping it from attacking).
You can also use the Dunmer's greater power, Ancestor's Wrath (for 60 seconds, opponents that get too close take 8 points per second of fire damage, once per day), if you find yourself near the frost dragon.
If you also have skill points and perks in Conjuration, the Flame Atronach (ranged fire attack) and the Dremora (wields a sword with Fire enchantment) can also help attack and absorb damage from the dragon. The Flame Atronach is weak to frost, though and will be easily dispatched by a frost dragon, if attacked. However, it is available at just level 25 skill in Conjuration, while to conjure a Dremora, you either need the Sanguine Rose or level 75 skill in Conjuration.