Unsurprisingly, most of the White Walker (The Others) abilities revolve around ice and cold.
- Create swords and other items from ice (seen in show):
Shaw: Do you know what substance an Other sword is made from.
Martin: Ice. But not like regular old ice. The Others can do things with ice that we can't imagine and make substances of it.
Raise dead humans and animals as wights (seen in show, unclear if all White Walkers have this power or just the Night's King)
Travel without leaving a trace in the snow (unclear if this is portrayed in the show)
"Bring the cold with them" / white mist (seen in show)
Speech, not exactly a "power", but as seen in the show it might just be thought of as screeching.
The Other said something in a language that Will did not know; his voice was like the cracking of ice on a winter lake, and the words were mocking. - A Game of Thrones, Prologue