To be fair, White Walkers makes more sense in context anyway given their appearance, the Other is usually only used in context to what is presumably the driving force, the proverbial Boss, behind the White Walkers, if R'hllor is to be believed. Though if Melisandre is to be believed..then Bran and Bloodraven are servants, if unwitting ones at best, of the great Other also, though given even within her religion the "Azor Ahai" legend is disputed as to who it refers to, i.e. either Jon Snow, Stannis or Daenerys, since all 3 are candidates for various reasons, some better than the rest, it stands to reason that not everything we know about anything in the world is clear cut, so the White Walkers might as well be the good guys, considering that, while they do attack and kill indiscriminately, 5 books in they havent really killed all that many people, let alone actually crossed the Wall proper, so may just be that they kill anything that invades their lands..and whereever winter is harsh, its their land (odd logic i know).
They havent so far been proven to be this nasty threat they have been made out to be, nor done anything that could be considered a direct declaration of war against the seven kingdoms to the south. In any case, white walker invasions, if they happen would be interesting, at least there should be, unless there already is, a event which fires during the later startdates, i.e. anything after Ned's Death and while Jon is still living that forces the whole mass evacuation of the wildlings to the wall, maybe even making all the provinces to the north ruins in turn, or white walker held if they do eventually come south in force.