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The answer to this question implies that Gared survived the White-Walker attack in the first episode of the first season because he outran them.
Which leads to the question, How fast can White Walkers run? (Let's limit this to when they are on foot instead of when they are on horseback.)
I'll accept answers from the TV series, but prefer answers from the books.
I'll start off by saying your answer appears to be based on a false premise in that Gared/Will didn't actually outrun the White Walkers. In the show it appears to let Will go as it is right next to him when it kills Gared. However, in the books it appears as though the Others aren't even aware that Gared was around as he stayed with the horses and wasn't near the other two when they were killed.
The fastest we see a White Walker move is actually in the prologue. There's some camera trickery going on here but they appear to be running faster than Gared/Will are through the snow but aren't moving faster than a human should be able to. This sets their lower bound at around a humans running pace.
You'll note from the scene that when the White Walker kills Gared it appears to spare Will. Will sinks to his knees and seems to accept his fate, however, the walker throws Gareds head at Will and doesn't seem to approach him. The next we see of Will is at the headsman's block. So it seems likely he was spared and didn't actually outrun them.
We know even less of the Others in the books. However, I was able to find this quote which implies that they are good runners but doesn't really give any information as to how quick they are.
The wights had been slow clumsy things, but the Other was light as snow on the wind. It slid away from Paul's axe, armor rippling, and its crystal sword twisted and spun and slipped between the iron rings of Paul's mail, through leather and wool and bone and flesh. It came out his back with a hissssssssssss and Sam heard Paul say, "Oh," as he lost the axe. Impaled, his blood smoking around the sword, the big man tried to reach his killer with his hands and almost had before he fell. The weight of him tore the strange pale sword from the Other's grip.
A Storm of Swords, Samwell I
(I have not read the books and thus I am answering from the show, hope this satisfies you).
In the S1E1 during the prologue it can be seen clearly that after the WW kills Ser Waymer Royce, Gared starts to run away and the WW can be seen clearly running at a pace almost similar to Gared's and catches him only when he stops out of exhaustion.
Also Will was not much further from the WW when he collapsed on his knees from the shock and exhaustion. Still he was able to make it to the Wall, which would have been quite a distance and he was already exhausted..
Similar was the case with Samwell when the WWs attacked the Fist of the First Men, he was just a few feet away from the WW, which was on a horse and yet he managed to outrun him and considering Sam's physical abilities and weight he would have never been able to outrun him.
This makes me believe that the WW spared Sam and Will and were not outrun by them. Why they did so is still a mystery.
