Cryomancy

Harness the powers of the frigid north as you ice your enemies. Siphon away thermal energies from your surroundings. Wield the power to freeze a threat in place, so it no longer is one. 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 Magicks

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.  In addition, whenever a creature takes cold damage within 15 feet of you, you may have that creature lose 10 movement speed. If a creature's speed becomes zero or lower this way, they become Frozen. A creature that is Frozen is restrained. A Frozen creature can use an action on their turn to make a Strength save against your spell casting DC 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.  Your spells now deal additional cold damage equal to your Proficiency bonus. You gain the ray of frost cantrip and shape water cantrip if you don't already know them. These spells are always prepared and do not count against your spells known.

Chilled Winds

Starting at 6th level, whenever you damage a creature with cold damage, that creature radiates a 10 foot radius swirl of frost around them for a number of turns equal to your Proficiency bonus. Whenever a creature enters or starts their turn in one of these areas, they take 1d6 cold damage. Overlapping areas stack their effect up to a number equal to your Proficiency Bonus. Each Frozen creature also sheds this area of cold in a 20 foot radius. Additionally Frozen creatures take an 1d8 additional damage from bludgeoning, piercing, slashing, force, and cold damage sources.

Ice Bringer

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 1d6 cold damage, plus an additional 1d6 cold damage for every level of the spell cast. If a Frozen creature is hit with this blast, parts of them shatter off, and their Armor Class is lowered by 1d4.

Permafrost

By 14th level, your cold magic surges through your body, lowering your temperature to impossibly cold levels. Plants frost over and die at your touch, and snow falls around you and wherever you walk. You are now immune to cold damage. In addition, you have become so cold that you can walk on water and other liquid surfaces, as it instantly freezes under your feet. You leech the warmth out of everything around you, dealing 4d4 cold damage to any number of creatures of your choice within 15 feet of you at the start of their turn. If a creature deals melee damage to you, as a reaction, you may deal 10d4 cold damage to them, and they become Frozen immediately. You may use this ability a number of times equal to one plus your Intelligence modifier per short rest. Any creature that is Frozen and starts their turn within 15 feet of you takes an additional 4d4 cold damage.