The user is able to generate and manipulate ice/cold within them in a way that allows them to shape the exhaling of the effect. These shapes can include bursts, streams, spheres, even a mist of it from the mouth.
As a Ice Devil Slayer, Silver Fullbuster (Fairy Tail), is able to use Ice Breath, in this case known as Ice Devil's Rage...
...which is then passed down to his son, Gray Fullbuster.
The Bewilderbeast (How to Train Your Dragon) breathing a powerful hydro blast, combined with its extremely cold breath, causing anything in its path to flash-freeze and shatter.
Enid (OK K.O.! Let's Be Heroes)
Cryogonal (Pokémon) using "Frost Breath".
Blossom (The Powerpuff Girls)
A Frost Dragon (Skyrim) breathing out ice.
Metarex Crystal (Sonic X)
Tundra the Walrus (Archie's Sonic the Hedgehog)
Dulcy the Dragon (Sonic SatAM) breathing ice from her nostrils.
Both Max and Phoebe (The Thundermans) can breathe a wave of pure cold from their breaths to freeze both people and ghost or project ice projectiles from their mouths. They can undo the effects by using their Heat Breaths.
Reycom's (Zatch Bell!) spells let him generate ice from his mouth.