Nothing of haze that I've seen and experience justifies haze being an ice-type move Unless there's another kind of haze I'm completely unaware of
Haze is an Ice-type move because of the cold air that is needed to provide a "hazy" atmosphere.
Source : Ohio Weather
Haze is an Ice-type move because it is the counterpart to Mist, some proof from Bulbapedia: >~Both are Ice-type ~Both avoid stat reduction ~Both can be learned simultanously by some Pokemon, for example Surskit at Lv 37 ~Both have the same PP ~Haze & Mist are known in Japanese as Black Mist & White Mist respectively
Source