As you may have guessed, the six ponies found the same place -- and the leaders began to fight over it. Even as the blizzard raced after them, chasing them into a cave for shelter, they squabbled and bickered, none willing to yield to the others.

The three leaders froze there. For they did not realize that the storm had a source: the windigos, who fed off their discord and antipathy, and brought a literal freeze to the world just as the hearts within it were frozen and barren.

At that moment, when all seemed loss and ponykind was to be doomed to eternal ice, their three companions, their loyal seconds, admitted to each other that, as it turned out, they didn't hate each other. In fact, they had common cause in how frustrated they were with their leaders, who had behaved so poorly all this while.

In that moment, when common cause because a connection between them, the three ponies discovered the Fire of Friendship. That was the key to repelling the windigos, who fled when faced with something so opposed to their very essence. When the leaders thawed out, they found themselves somewhat more open to cooperation, and taking the lesson to heart, ponykind joined as one to found the nation of Equestria.

[Celestia blinks once at the end of that recitation, then smiles ruefully.]

The pageant tells it better.