This is really a fairly simple question... In the most recent episode of Game of Thrones, we see the army of the dead (I'm assuming) marching south. We have seen from plenty of past episodes that they are capable of running. As far as I know they have no need to eat or rest to keep up their energy, so why don't they run everywhere? It would be much quicker.
While there is a great deal of mystery surrounding the origins of the White Walkers, they do not seem to be in any hurry...
The Long Night was thousands of years ago.
Now, six thousand years later (or eight thousand as True History puts forward), the Wall made to defend the realms of men is still manned by the sworn brothers of the Night's Watch, and neither the Others nor the children have been seen in many centuries.
The World of Ice and Fire - Ancient History: The Long Night
It took Mance Rayder 10 plus years to join the clans together.
It has been roughly 2 years since the beginning of the series (i.e. when we see the White Walkers in Season 1, Episode 1)
The Night's King seems to still be gathering strength. Creating new White Walker from Craster's babies, adding to the army of wights (Hardhome), etc.
The Wall has magic imbued into it:
But one thing I will say, for what it's worth -- more than ice went into the raising of the Wall. Remember, these are =fantasy= novels.
Quote by George RR Martin
Magic that is most likely related to White Walkers, specifically keeping them out (remember when Bran reaches the Three-eyed Raven's cave and there is a magic barrier):
Melisandre smiled. "Necromancy animates these wights, yet they are still only dead flesh. Steel and fire will serve for them. The ones you call the Others are something more." "Demons made of snow and ice and cold," said Stannis Baratheon. "The ancient enemy. The only enemy that matters." He considered Sam again. "I am told that you and this wildling girl passed beneath the Wall, through some magic gate."
A Storm of Swords - Samwell V
So it is my guess that the Night's King is waiting for something, most likely something magic to happen to allows the army of the dead to mount their full scale assault on Westeros.
But reaching The Wall early will not do them any good. The wights can be destroyed by regular weapons. The White Walkers can be destroyed by dragonglass and Valaryian Steel, and the Night's King knows the humans have both these weapons. Again, there is also magic involved, so pure speculation is if magic raised them there might a magic timer as well...
They are utilizing a method called "persistence hunting". It operates on the premise that your prey can't escape and so you'll get to your destination in the most efficient manner.
I'm reminded of a description I read about how it might look from the point of view of the hunted
can we talk about how pursuit predation is terrifying
it’s one thing to face down a cheetah, which will slam into you at 60 mph and break your neck
it’s another thing to run very quickly to get away from a thing, only to have it just kind of
to have it be intelligent enough to figure out where you are by the fur and feather you’ve left behind, your footprints and piss and shit, and then you think you’ve lost it and you bed down for the night but THERE IT IS
WHEN YOU WAKE UP
and you split! again! but it keeps following you. always in the corner of your eye. until you just
And that's the premise here. The show is using the sheer inevitably of the army of the dead to build dread (for the audience mostly). It doesn't matter when they get there... because they will get there.
In response to some of the points brought in in comments:
The army of the dead is just that, dead. Their bodies are no longer capable of healing themselves. Running is a reasonably traumatic experience on the body, and since they can’t heal the damage it induces, and their quarry can’t get away, it makes no sense to run. Efficiency is not limited to energy expenditure. Efficiency means the most equal balance between loss and gain. In this case, loss is wear and tear on the reanimated corpses, and gain is killing humans. Increasing speed does not improve the gain at the same rate it increases the loss. Ergo, it is less efficient for the army to run while not in a battle situation.