Kekkei Genkai of the Yuki Clan
The Ice Style is the Kekkei Genkai of the Yuki Clan, the ice they create is largly immune to fire-based jutsu, only melting slightly when coming into contact with flames. Using this special ability, the Yuki Clan's Haku developed the Secret Jutsu: Crystal Ice Mirrors Which allows the user to create any number of mirrors made of ice to use as a shield or trap an opponent.
None-Kekkei Genkai of the Hozuki Clan
There a clan that can use Ice Style without Kekkei Genkai, the Hozuki Clan of Kirigakure can use the nature by following the ways and possessing the abilities of the Ice Dragons, during the finish their training, they are now official Ice Dragon Wielders, so basically to the Hozuki Clan, Ice Style ninjutsu are Hiden Jutsu.
Although there is another way a person can obtain this ability to use this nature (and a cure for the Diclonius Virus by removing their horns), is to inject an ice Dragon's blood into the veins. There are only a few people who have done this before in history and the present day.