Cryomancy

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 2nd 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, you deal addition damage equal to your Proficiency bonus.

When you cast a Wizard spell with a spell slot, 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. This spell is always prepared and does not count against your spells known.

Frozen Solid

Starting at 2nd level, your icy magic slows the world down to a crawl. Whenever you deal cold damage to a creature, you may have that creature lose 10 feet of movement speed for 1 minute. If a creature's speed becomes zero or lower this way, they become Frozen.

A creature that is Frozen is restrained and takes 1d4 additional damage from bludgeoning, force, and cold damage sources.

At the end of each of their turns, a Frozen creature makes a Strength save against your spell casting DC to attempt to break free of the ice. If they succeed, their speed is returned to normal and they must have it lowered again to become Frozen once more.

Chilled Winds

Starting at 6th level, painful cold winds swirl out around your frozen victims. Frozen creatures produce a sphere of frost around them in a 10 foot radius. Whenever a creature enters or starts their turn in one of these areas, you may have them take 1d4 cold damage.

Cold Snap

Beginning at 10th level, cold magic runs through you with such fervor that it bursts forth whenever you channel arcane energies. Whenever you cast a spell, you create a blast of ice and snow in a 5 foot radius centered on you.

The radius increases by 5 additional feet for every level of the spell cast. Any number of creatures of your choice that are hit with this blast take 1d4 cold damage, plus an additional 1d4 cold damage for every level of the spell cast.

Absolute Zero

By 14th level, your cold magic surges through your body, lowering your temperature 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.

Whenever a creature enters or starts their turn within 15 feet of you, you may have that creature take 1d4 cold damage. When you reduce a creature's movement speed with your Frozen Solid feature, you now reduce its speed by 20 feet instead of 10.