Decided to give Druid a try, making use of my Onyxia card.. the deck I have is slow going, I'll have to put some cheaper minions in there. But I had quite a nice run at the end.
Hunter had 28 health and 4 minions up. I was toast on this turn. But I got my draw.
Onyxia + Mark of the Wild + Soul of the Forest + Savage Roar to clear the board. (I didn't take a screenshot before this because I wasn't sure if it was going to work)
2nd turn: A board full of Treants and Savage Roar again (you can see he tried Hunter's Mark). I only realized now that I didn't need to use it the second time but why not since I drew it :P
Edit: Actually I have plenty of cheaper minions in this deck, I just didn't draw a single one all the way up to turn 10.