Mindgames seems like a really odd choice for a control Priest. But, I'm no Priest expert.
This is my Paladin deck. Again, I'm no expert, but I do pretty well against Priest. With the 2 Kodos, you can easily eliminate their health-buffed Northshire Clerics. I will actually keep a Kodo in my opening hand if I have one. If I'm going second, I will keep either Tirion, Ironbeak/Spellbreaker, or Kodo. I won't mulligan for any of those, though.
|Minion (20)||Ability (8)||Weapon (2)|
My deck is tech'ed more for aggro. So for control Priest, I would drop Ironbeak for a Spellbreaker, Unstable Ghoul for a second Shade of Naxx, and I would also drop the Sludges or Senjins (maybe one of each) for Sunwalkers. I might also drop that second Guardian of Kings for a Spectral Knight. Spectral Knights and Faerie Dragons are really hard for Priest to deal with.
Assume they are going to Thoughsteal Tirion, and always, always, always hold your silence until they play Tirion against you. Unless you are confident about your win in some way that the Priest having Tirion or the Ashbringer won't matter.
You're giving the priest so many great Thoughtsteal targets that can be used against you -- The Black Knight, Acidic Swamp Ooze, Tirion, Ysera, Faceless, even those Zombie Chows if they combine them with Auchenai.
My last thought here is that if the Priest plays Northshire Cleric on turn 1-3 or something, and you don't have a minion on board with high enough attack deal with it (like a Wild Pyro), do NOT use your hero power. If you put out a dude on turn 2, for example, Priest just runs their Cleric into it and heals to draw a card. Also be aware on turn 6 Cabal Shadow Priest is now an option, so dropping a late Acolyte of Pain might not be a good idea unless you have a silence or some way to deal with it on the next turn. You just want to limit their card draw as much as you can.