Why this change in the White Walkers physical appearance?

Question

In Season 1 of Game of Thrones we only ever see the shadowy figure of the White Walkers as they are running and when one confronts Will and Gared.

When I watched the prologue back, at around 5:41 in this clip, you do see a very quick glimpse of a White Walkers face as it kills Ser Waymar Royce.

However, in the later seasons the White Walkers have changed and now look like the following.

Of course even later on the White Walkers have gone shopping and now have some armour.

Why this change in the White Walker physical appearance?

Answer 1

It appears as though the change was only down to the producers not really liking the initial design for the White Walkers.

“This sequence was meant to be shot in Iceland in November. But some of the scenes didn’t quite work out and the executive producers wanted a re-shoot, so they set up this reshoot in London. The producers and creatives were not happy with the White Walker costumes from season one; they wanted to redesign the look and it took a bit longer than expected.
_{Fast Company, Collaboration Isn’t Always Pretty–Behind The Emmy-Winning VFX For “Game Of Thrones”}

On a side note in the Season 2 Episode 10 ending you see more than one White Walker but because of the redesign they only had one costume so it's the same actor but duplicated.

“It was challenging because we only had 50 extras, which required crowd replications. They wanted about 1,000 zombies or wights, as they called them, with about 10 to 30 White Walkers mixed in, and we only had one White Walker costume that had to double for all these white walkers.
_ibid