Okay so I just beat Noth using this deck (or actually a slightly weaker version of this deck). Proof:

Strategy

This is a deck that wants board control. You don't really go for face until you have a solid grip of the board. The idea is to use removal for Noth's early minions so he doesn't snowball too much, and then ramp into your big beefy minions that you can use for favorable trades that do not trigger his hero power. Use your buffs in such a way that as few of your minons as possible die. P.S Noth runs The Black Knight, beware.

Mulligan

When I won, I had Wild Growth on turn 2. I think this is pretty vital -- you need to be able to ramp up quickly or you will fall behind, so it might be an idea to concede until you get Wild Growth on your starting hand. Other good starting cards are Claw, Innervate and your cheapest minion which is Druid of the Claw. Any removal card is ok to keep too.

Alternative cards

Sylvanas Windrunner would be absolutely amazing in this deck, you can swap her for a Frost Elemental. I wasn't using her because I don't have her. Same with The Black Knight.

 was running 2x Ironbark Protector instead of Ancient of War -- only because I don't have the Ancients. They are most definitely better than the Ironbark, but, yeah, you can still beat him with the Ironbarks.

You can probably add in another Sea Giant and change out any of the big minions. Most of them should do well. However, I must say that Ysera was pretty amazing. She killed off a lot of Noth's board and I drew so many dream cards off of her. Ragnaros was also great to snipe off a lot of stuff once I had my taunt wall up.

Good luck!