Cold is one of the types of Elemental Damage. Not only is it just damage, but it also has slowing effects on you or on the monster that takes it. The effect is visible by a blue hue, and is commonly known as Chill. Frozen effect is a more powerful consequence, often added to Cold skills. Usually Cold is associated with colors blue or white.
Cold damage is taken rather seriously by players because of its versatility. Cold is not known for its damage range or amount but more for its effects of slowing, freezing and shattering opponents.
Cold damage is especially useful for crowd control in both single-player and multiplayer experiences. If a monster takes Cold damage, it might become totally frozen and stay still for some time. Super Unique Monsters, on the other hand, cannot be frozen. They can only be slowed, reducing their movement and attack speed. If you take Cold damage from a monster or from PvP, you will just slow down.
If a monster dies as a result of taking Cold damage, it will sometimes shatter into pieces, leaving no corpse. This is especially useful when fighting against groups that can resurrect slain comrades like the Fallen and their Shaman. The shattered bodies simply fall apart into ice shards, which quickly melt into the ground and leave no corpses, which could be revived by the Shaman.
Cold damage is used by the Sorceress, Paladin, Druid, Amazon and Assassin classes. Out of these, the Sorceress has the greatest repertoire of Cold Spells in a single skill tree than all the other classes combined. This makes her an ideal candidate for a crowd controlling member in parties.
In Diablo III, Cold damage is used by all classes except Crusaders, often chilling or freezing its target. Critical Hits from Cold skills freeze the slain target solid, making it shatter afterwards. Note that any Cold damage hit has a chance (lower than the Proc Coefficient, though) to Chill enemy on hit.
Andariel's Visage, Azurewrath, Utar's Roar, Stone of Jordan, Frostburn, Wrath of the Bone King, Winter Flurry, Etrayu, Gesture of Orpheus, Lidless Wall, Swamp Land Waders and Holy Point Shot are the items with unconventional bonus to Cold skills damage. Talisman of Aranoch amulet will render the character completely immune to Cold damage (the attacks will actually heal the Nephalem).
Cold has many effects, but the most annoying one is their slowing effect. This is especially true in the case of Cold Enchanted monsters. They have been known to slow the pace of the game forcing players to lose precious time in their games.
Cold is used by the Lord of Pain, Duriel, in the form of the Holy Freeze aura that slows down the player character to a grinding halt, often killing the player before Tal Rasha's Chamber is even loaded.
The Lord of Terror himself, Diablo, uses Cold damage in his slowing Cold Touch attack. He raises his right hand in the air like the initiation of the deadly Red Lightning Hose, but his palm glows an eerie blue before he strikes down on the player with all his force. Most players avoid this due to the initiation action making players run before being struck by a possible red death.
The Lord of Destruction, Baal, also uses Cold in a more noteworthy style in his Hoarfrost attack. A crushing triangular wave of cold is launched towards the player, causing heavy damage, slowing and a severe knockback. A very deadly attack that can be seldom avoided at range.
Izual is known to have great affinity with Cold, causing the chill of hell sap the life from his victims.