For that kind of approach you have three options.
#1: mirror image. 0-2 cards don't damage a cleric, so he'll have nothing to draw cards from. You can build your board behind the mirror images, and when they're powerful enough to finish off the cleric, do so.
#2: Delay and play nothing for a while until you have enough in your hands to force most of his minions off the board and put a solid board presence with only the cleric to face. being 1 damage only he won't be able to do much to your board, and from there just work on building board presence until you can kill it (if it takes a couple turns, well it takes a couple turns). Usually this means that until turn 4-5 you won't be able to play anything other than removal. Do this if you don't have a fast answer to put on the board early on.
#3: this is only if you're running a deck with enough minions (which you should after the pyro nerf, anyway), and if you happen to have those minions in your hand. Accept he's going to maybe draw 1-2 cards and have that advantage over you, at a cost. That cost is that to get his card he has to heal a minion, that's 2 mana off his budget, and that means for instance that if he does turn 1 cleric-coin-shield, and you place a 3-2 on the board, he'll be down to 1-2 and will have either to heal (ending his turn), to 1-3 but draws no card (if he uses SW pain and probably too if he uses smite), or to 1-6 but no card (if he double-lifes it).
If he does the first , he'll have a 1-4 on the board. Slam your now 3-1 versus him, and hero power, cleric gone. Or maybe play a sun cleric on the 2 mana, and you'll keep it as a 4-1 after smashing the cleric. He's won one card, but lost the cleric and if you used hero power to finish it off you still have room to maybe play a mana wyrm.
If he does the second, just play a 3 mana minion, or another 2 mana 3-2, and proceed to do the same. He's gotten no cards and you have a 3 mana minion on the board.
If he does the third, do as in the last one. Build your board presence while he buffs the minion and keep on smashing for more than 2 damage on it. Eventually it'll go down and when it does you'll have 2 or 3 minions on the board while he has none...that's if he wants to exploit the card draw ofc.
The cleric play has some inherent advantages towards the priest as the more cards he draws the more powerful he'll be as turns go by, but it means that to keep the cleric alive and to draw those cards he can't play almost anything else. Use that to build control over the board, and maybe later you can use arcane intelect to close down the gap in cards. It usually also means that the game is going to be long, and that favors him, but also you, as Mage is increasingly powerful as the game goes into the lategame.
If you're running one of those douche freeze decks, however, you're doomed as you won't have enough minions, and I don't feel simpathy for you anyways xD. Freeze decks are amongst the most full of BS ones in this game, so unfun to play against and it's weak point (that leaves early game to basically let the other guy whatever he wants without a proper answer on the board) becomes it's death sentence against a buffed northshire. Rightly so. I hate freeze mages. With a passion.
Edited by RAMJB on 1/19/2014 5:12 PM PST