I've searched up Vannilite's, Vanillish's, and Vanilluxe's Abilities, and Vanilluxe can get Snow Warning and Ice Body. Do you get the Ability as a Vanillite, or there is a chance you can get the Ability once you evolve it into Vanilluxe?
Vanilluxe can't have snow warning before gen 7. White is a gen 5 game.
You cannot get a Vanillite with Snow Warning. According to this Snow Warning page on Bulbapedia, the only Pokemon that has Snow Warning for Vanillite's evolution is Vanilluxe, who doesn't gain the ability until Gen 7.