If you can find or make some equipment with either magic or frost resistance, their breath attacks will do less damage to you.
Having a companion with you can help by tanking the dragon for you, so you can attack
it's side, so it can't hit you with its tail.
You can also bash them with a shield during its breath attack to stop it prematurely.
It really depends on what kind of character you are.
gaming.stackexchange.com/users/22971/iLevin
A great way is to use "Spell breaker"
It creates a ward that blocks any magic attack up to 50 damage.
This can be used on any dragon except ancient.
gaming.stackexchange.com/users/23181/Harrison Miller
Another strategy not mentioned is to use the dual casting destruction perk Impact.
Assuming your playing a magic-using character of course.
Impact as I understand it normally does not stun dragons, however once you put points into the appropriate "additional damage" perks of whatever school your using (fire, frost, or lighting)
it will.
While the conditions to meet this status are hazy to me, I know for a fact it works as I've stun-locked dragons many times.
Simply stun them as they are about to use their breath attack, and voila.
gaming.stackexchange.com/users/15095/Ender
Rather a high price to pay, but becoming a vampire does the trick.
Vampires are 100% resistant to cold, as I found out after several minutes wondering why getting my arse repeatedly frozen by a dragon was doing me no harm :)
gaming.stackexchange.com/users/23218/Rob Agar
Use magic and frost resisting potions and equipment .
You can find a damage reduction calculation here: Is Resist Magic multiplicative or additive?
Frost dragons are weak to fire .
So you should use fire spells .According to the UESPwiki entry it is 25% and it has a 50% restistance to frost.
So don't use frost spells.
You can increase the weakness using an aversion to fire potion .
Using a flame atronach as a damage addition and diversion could also be helpful.
You can cast this with a scroll, a staff or spell.
gaming.stackexchange.com/users/9781/Tom
Defense 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).
Offense 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.
gaming.stackexchange.com/users/4797/galacticninja
Well a problem with a frost Dragon ah, Here are some Tips:
They are like any other Dragon.
They are vulnerable to fire and Sparks.
Once in a while it will stay still to attack.
Use that as one weak point of Dragons.
As soon as it crash lands (When it cant fly) stay away from the tail and the head.
Although you may still get damaged, it will be better then getting eaten or sent to the moon.
gaming.stackexchange.com/users/68187/TheFez
I find these types of Dragons really difficult to face. One strike with their frost breath wipes out most of my health. I have beaten some before, but I need easier ways, so feel free to tell me anything-Thanks     I am a Dumner or the Dark Elf btw and I use all magic, but mostly destruction.
How do you beat frost dragons in Skyrim?
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gaming.stackexchange.com/users/23086/xFaLLeN_Eternity
Find some equipment with magic or frost resistance and have a companion with you to tank the dragon for you. They are vulnerable to fire and sparks. Frost dragons can be defeated by following a wide range of tactics, combined with specific gear.
The community is giving details regarding different strategies to beat frost dragons.