Cryomancer

Many disciplines of the arcane teach their students how to add energy into the world. Cryomancy, however, teaches the art of pulling energy away. Specifically, the school of magic teaches how to siphon away thermal energies. When a wizard can simply freeze a threat in place, it no longer becomes a threat. Many foolishly only see this magic as beautiful, and it is, but within the beauty of all that shimmering ice, is a slow and shivering death.

Frigid Magics

When you choose this school at 3rd level, you learn to pull the thermal energy out of the air with your spells, chilling your enemies to the bone. Whenever you deal cold damage with a spell, you deal additional damage equal to your Proficiency bonus.

When you cast a Wizard spell of 1st level or higher, you can temporarily replace its damage type with cold damage as a free action for that casting. You may replace the damage type a number of times equal to your Intelligence modifier per short rest.

Finally, you gain the ray of frost cantrip if you don't already know it, and it is thereafter always prepared.

Numbing Cold

Starting at 3rd level, your icy magic saps the strength and will of your foes. Whenever you would deal cold damage to a creature with a spell of 1st level or higher, you may prevent the damage and instead have the creature make a Constitution saving throw against your spell casting DC. If they fail their save, they become Numbed.

Whenever a creature that is Numbed makes an attack roll or rolls for dealing damage, it must subtract 1d4 from that roll.

At the end of each of their turns, a Numbed creature may repeat their Constitution save against your spell casting DC to attempt to shake the numbing sensation. If they succeed, they are no longer Numbed.

Chilled Winds

Starting at 6th level, painful cold winds swirl around you and bite into any would-be assailant. As a bonus action, you may produce a 5 foot Emanation of icy cold for one minute, and it moves with you. Whenever you cast a spell of 1st level or higher, this Emanation's size doubles to 10 feet until the start of your next turn. 

Whenever the Emanation enters a creature’s space for the first time in a turn (or vise versa), or a creature ends its turn in the Emanation, you may either have the creature take cold damage equal to your Intelligence modifier or have them make a Constitution saving throw against your spell casting DC. If they fail their save, they become Numbed. You may project this Emanation this way a number of times equal to your Proficiency bonus per long rest.

To the Bone

Beginning at 10th level, the cold magic you wield leaves your enemies with crippling shivers. A creature that is Numbed must now subtract 1d6 from their attack and damage rolls, instead of 1d4.

You now also gain a resistance to cold damage.

Absolute Zero

By 14th level, your cold magic surges through your body, lowering the surrounding temperatures to impossibly cold levels. You leech the warmth out of everything around you, plants frost over and die at your touch, and snow falls around you and wherever you walk.

The size of the Emanation from your Chilled Winds feature is now 15 feet, and now doubles to 30 feet when you cast a spell of 1st level or higher.

Additionally, whenever a creature makes a Constitution saving throw against becoming Numbed, or to end being Numbed, you may use your reaction to have that creature make their save with disadvantage. You may use this feature a number of times equal to your Proficiency Bonus per long rest.