According to the Sun and Moon story, Alolan form Ninetales can produce ice crystals from its fur. It can use them to block attacks or turn them into powerful ice missiles which can shatter rock.
Fairy-types have proven themselves to be fairly powerful in the X & Y games, so it's pretty cool that Ninetales gets an upgrade in that way. I'm not so sure how I feel about Vulpix and Ninetales becoming Ice-types. But, this new typing gives them access to many new and powerful Ice and Fairy type-moves. They are no longer weak to water, but are now weak to Fire, Rock, and Steel. These new strengths and weaknesses entirely change entirely how Ninetales is utilized.
Of course, these changes only apply to the Vulpix and Ninetales actually caught in Sun and Moon. With the new typing, Alolan Ninetales became quickly overused in the competitive meta for Pokemon Sun and Moon. In fact, it is the only Pokemon that can use both the Aurora Veil move and the Snow Warning ability. Aurora Veil halves damage from incoming attacks to your team temporarily. Snow Warning summons Hail, which damages non-Ice type Pokemon for 1/16 of their HP each turn.
Alolan Ninetales also has access to a powerful attack called Freeze-Dry, which is super effective against Water-type Pokemon. According to Smogon, Alolan Ninetales is considered too powerful for many competitive Pokemon battle formats. Even if you don’t care about battling competitively in Pokemon, Alolan Ninetales is definitely a Pokemon to consider for your Sun and Moon team in the future.