Let me start by stating that the Taunt Warrior usually has the upper hand in control matchups. When finding yourself in unfavorable matchups you usually have to take more risks than you would take in even matchups. Don't be afraid to make all-in plays if you think that there is no other way to win at some point.
To correctly approach a specific matchup you need to identify either side's wincondition. For the Taunt Warrior this is obviously completing the quest and closing the game out with the Ragnaros heropower.
You wincondition is controlling the board and finishing the game with minion attacks. This is actually true for all your matchups, since you have no other tools to win the game.
This already gives you a rough idea of your general gameplan: Aggressively pushing for board control and keeping it by using your powerful AOE-spells until you minions represent lethal damage.
You absolutely must secure board control in the early game and pressure the Taunt Warrior. Always keep in mind that most of the Taunt Warriors run two Brawls, so make sure to not overextend. However don't tunnelvision on playing around the second brawl, you probably have to take the risk of them having it ready at some point.
In the midgame, focus on maintaining board control by using Blizzard and Flamestrike. The perfect scenario is having a good board by turn 5 and then following this up with Blizzard and Flamestrike in the following turn.
- Don't be afraid to use Fireballs and Frostbolts early to make sure that the Warrior can not take over the board early.
- Always keep in mind that board control is your wincondition. If you lose it, you will probably lose the game, unless you manage to finish the Warrior off with your burn spells.
- Don't use your weapon-remove on Fiery War Axes, unless you absolutely have to to maintain your board. Most Taunt Warriors run Gorehowl, removing this weapon is crucial to keeping your board intact through the midgame.
Your deck has a lot of one-ofs which is not really common outside of Reno decks (RIP). On the one hand this lets you fit more tech-cards but on the other hand this makes your deck very inconsistent.
You definitely should run two copies of:
- Fireball - More burst, opens up a fallback wincondition if you fail to control the board.
- Frostbolt - Same as above and additionally serves as a great early game removal tool.
- Mana Wyrm - Together with Frostbolt this card can get insane trades in the early game and secure board control.
- Arcane Intellect - Reliable card draw in the mid- to lategame.
- Water Elemental - Overall very solid minion and great against weapon classes. Any board-focused deck should run two of those.
This adds 6 more cards to your current deck, so I propose to cut:
- both Cone of Colds - This card is only really useful for decks that want to stall the game, like Freeze Mage. But since stalling the game is the complete opposite of your goal and actually the Taunt Warrior's wincondtion, this card does not help you in any way.
- Counterspell - While mage secrets have the strongest effects out of all secrets in the game, they are also fairly expensive with 3 mana. Running secrets without cards like Kirin Tor Mage is usually not a good idea, since you lose a lot of tempo when you pay 3 mana without any effect on the board. Decks like Freeze Mage are okay with that, your deck is not.
- Stonehill Defender - While this is a great card in defensive decks, it's board impact is very insignificant for it's mana cost.
- Flesheating Ghoul - This card is only good if it gets the right setup which you should not rely on.
- Shimmering Tempest - Bad stats for a 2 mana minion and it's effect might not come into play later in the game, depending on the manacost of the generated spell.
Depending on the type of decks you encounter on the ladder, you should merge some of your early game one-ofs into two copies of the same card. This overall makes your deck a lot more consistent and increases the odds of drawing specific cards in the early game.