What is the name of the realm of ice in Norse cosmology?

The realm of ice in Norse cosmology is called Niflheim.

Niflheim, or Niflheimr in Old Norse, means “world of mist” or “home of mist.” It is portrayed as a primordial region of cold, ice and darkness. In Snorri Sturluson’s Gylfaginning, Niflheim is one of the two early cosmic realms, set opposite Muspelheim, the realm of fire. Their opposing forces meet across Ginnungagap, the primordial void, and help bring about creation.

Niflheim contains Hvergelmir, a spring or well from which numerous rivers flow. These rivers are associated with Élivágar, whose icy and poisonous flows contribute to the formation of rime and frost. The primordial being Ymir emerges when the cold of Niflheim encounters Muspelheim’s heat.

Niflheim is sometimes confused with Hel or Niflhel. Snorri’s account links Niflheim with the domain of Hel, ruler of many of the dead, but the surviving sources do not always use these names identically. Muspelheim is its fiery counterpart, while Jotunheim is associated with the jötnar, or giants. Thus Niflheim is the best canonical answer for the icy realm.