So I chose Dunmer as my character for the resistance to fire. I figured it would be good to fight mages and even more so to fight dragons.

However out of 9 dragons, I've had zero fire dragons. All of them have had frost breath... Did my race change what dragons appear?

I'm Imperial and I mostly fight ice mages and ice dragons myself.

I think level (might) affect dragons. I've played as an Altmer twice in a row... on my first playthrough I almost never got a generic "Dragon" and even then "X Dragon" appeared only after the MQ and Civil War quests were finished (not including the quest-controlled dragons).

But for my current playthough, I've gotten a few generic dragons and one Frost Dragon (and I'm level 30).

It's random, you only see certain dragons after you hit certain levels. But you can always get lower level dragons.

Don't think so, level 53 Breton and the majority of what I encounter is Frost Dragons.

The dragon system is level based. I'm level 44 and all I see is Elder Dragons and a sometimes an Ancient Dragon.

I think whether they breath fire or ice is random, so it seems you're getting unlucky
I just know as you level, you get blood dragons, elder dragons, then ancient dragons.

Ancient dragons are fun

Although one thing that's annoying about dragons (at least in my game): After I take a dragon to about 25% health, it immediately flies off and attacks the next closest mob (usually a bandit camp or something)

The amount of effort I have to making running down the dragon to absorb its soul is totally un cool