You want some board control early game. Keep First Flame, Primordial Studies, Ignite, Runed Orb, 1 Frostbolt. Always keep Incanter's Flow if you have The Coin. You never want to keep Emperor Thaurissan or Refreshing Spring Water. I mostly keep an Ice Block to play it on curve but you can send it back sometimes as you will end up drawing into one eventually.
Against Paladins, Warriors and Hunters you can keep a Cone of Cold, try and play it with some spell damage on your board, ideally from Primordial Studies. You can Ignore 1, 2 attack cards initially if you have Ice Barrier and save damage spells to kill any early threats. Play card draw or Primordial Studies, face the damage for a turn or two and wait for a threat before playing a First Flame or Frostbolt on it. Always prioritize clearing the board with face hunter, don't save your damage spells.
I haven't faced many shamans, I will look at my HS Replays and update the mulligan if I find something useful.
With every other class, keep cards that prioritize quest completion.
Against Warlocks you want to start burning their health from early on. Try to complete your quest also but go face with most spells. I usually have the Warlock down to <15 health by turn 5 thanks to some assistance from the Warlocks themselves. Use Primordial Studies and choose the option with the best value for mana. You can keep Bloodmage Thalnos if you're feeling extra spicy.
Against Elwynn Boar Decks, save all your cheap freeze spell for late game if they get a good tempo early. Never leave a minion alive on your side of the board. Kill off any minions from Primordial Studies with your spells and complete the quest asap. Once they get Sword of a Thousand Truths, you are back to 1 mana crystal next turn. Hopefully by then you have most cards ready and discounted. Freeze them every turn you can't kill them. TBH it's game over once they get the sword but their hands are usually empty by the time they obtain it and you get to buy some time with your freeze effects. You can cast an anticipatory Freezing Potion or Ice Lance if you think they are going to obtain the weapon next turn and buy even more time.
More matchups soon..
You buy time to finish the questline before you draw your buffed and discounted spells and kill the opponent in one turn.
You can do 30+ damage with 2 mana crystals if you play it right. And 30+ with 8 mana if you don't die and draw your combo.
A recent 2 mana OTK: https://hsreplay.net/replay/d5mxrLDWAXEyPRFwW4hs6L#turn=9b
Save Ice Lances for an activator. Use 1 if absolutely necessary. Use Hot Streak to progress the quest if you have to. Save 1 Frostbolt. Save 1 Cram Session to use after Arcanist Dawngrasp. But don't save too many cards, or you risk burning cards with a full hand. You can cast 1 Fireball on any early threats but try and get quest value out of it. Cycle Ignites early and do it before playing Incanter's Flow if you have the mana.
You can use the Sorcerer's Apprentice mid-game to finish the quest or as a threat that takes some damage instead of you. Playing the Sorcerer's Apprentice right can win you the game. Incanter's Flow is always a higher priority over quest efficiency, so even if you've already played an arcane card, you play Incanter's Flow if you draw it.
Turn 8, 6 mana otk: https://hsreplay.net/replay/pfyDmWZbn9Xmt99AhuJ2RC#turn=8a
Turn 10,6 mana otk: https://hsreplay.net/replay/tk92VboV2AdvHqQVKxd4x9#turn=10a
Turn 10,9 mana otk: https://hsreplay.net/replay/6M2YDPv92WvGxniyqkhw7B#turn=10a
Turn 9, 4 mana otk: https://hsreplay.net/replay/FLKCyz5Egv2UAieE8HHDx7#turn=9b
Turn 9, 7 mana otk: https://hsreplay.net/replay/HJsMGoUzqgfcArCEpZ5ndn#turn=8b
Turn 6, warlock kill: https://hsreplay.net/replay/oFh2wbxBjcgP694yAVvpr2#turn=6b (quest incomplete)
Turn 7, warlock kill: https://hsreplay.net/replay/zQdtGXEi3baKuf4wxfsycc#turn=7a (quest incomplete)
Turn 10.warlock kill: https://hsreplay.net/replay/QYS6wGkZCBPRuk6S4E8At6#turn=10a
Feel free to remove Emperor Thaurissan and replace him with whatever you like, he can sometimes be a tempo breaker for you, I use him as a threat.
You can replace any card you feel you need to. I like Cone of Cold, and that's why it's in there. You can replace it with a Frost Nova if you want or an even lower mana card. You can swap out 1 Incanter's Flow with a Sorcerer's Apprentice too.
This deck is strong against some meta decks on the ladder. It's version 5 of my freeze mage from 2016-17 standard, now including the current standard quest. The previous, very recent iteration ran classic Alexstrasza, Doomsayer, and Frost Nova. I retired Alexstrasza from the deck because for 9 mana, you can OTK the enemy if you complete the quest sooner.
It's a freeze mage archetype because you have 2 Ice Blocks, 2 Ice Barriers, and you may need to extend your turns to late game. Then there's the OTK. Since Incanter's Flow's nerf, quest mage has become slower. This deck is almost as fast as the standard quest mage. I usually finish the questline in turn 5, 6 or 7 sometimes even on turn 9. The Ice Block provides a safety net for a late questline finish. However, the priority is to finish the quest ASAP, which is your win condition.
I consistently OTK Paladins, Hunters, Priests, Warriors, Rogues and usually kill most questline warlocks even before completing my quest. Hunters can be a difficult matchup. Quest warrior is a pain. The mage vs. Mage game is very interesting. You want to burn the enemy's health a bit as you set up your OTK. But with Priests, you don't want to dump a Fireball on their face turn 4. For Warlocks, however, that kind of behavior is mandatory. Sometimes you may have to play around Reno Jackson, so don't dump everything early without a plan.
As you always play Ice Block on the curve, cards like Kezan Mystic, Flare, Eater of Secrets, Chief Inspector, SI:7 Infiltrator, and Zephrys the Great can be problematic. So if the Ice Block gets removed right before the opponents' killing blow, it's concede town. However, this is rare as most players don't seem to expect an Ice Block. I've had a few hunters Flare me down right before killing me which was fun.
Like other, more vanilla freeze mage decks, you often win the game at 1 health. Previous experience playing a freeze mage would help in planning your OTK with this deck. Ice Block is like a 3 mana Time Warp from the quest Open the Waygate, and you have two. Even if one gets eaten, save the other for right before the end. Also remember you can die on your turn so fatigue damage will kill you.