Since the question is tagged with A song of Ice and Fire, I will get in some perspective from the books.
In a Feast for Crows Maester Aemon Says:
I should not have left the Wall. Lord Snow could not have known, but I
should have seen it. Fire consumes, but cold preserves. The Wall . . .
but it is too late to go running back. The Stranger waits outside my
door and will not be denied.
He was referring to his physical state which started getting worse after he left the wall. If Cold can preserve an old man well into his hundreds from death what do you suppose happens to a being which is completely made of Ice and cold?
The Others are not dead. They are strange, beautiful… think, oh… the
Sidhe made of ice, something like that… a different sort of life…
inhuman, elegant, dangerous.
But while the cold did not stop aging process for Aemon, it most certainly protected him from death from effects of Old age.
It must be noted that show does not differentiate between Others and Wights. Wights are resurrected dead men while Others are the magical creatures who perform that resurrection.
As Melisandre said:
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
We do not know who was the first of the Others but we do know where did they come from. About 8,000 years ago, Long Night fell on Westeros (And most probably rest of the World because similar legends are found in traditions of Yi-ti and As'shai). The demons now known as the Others came from the farthest reaches of the North known as Land of always Winter. They were however defeated and were never heard of again until the events in ASOIAF.
But even in the Books, we know The Others do something with infants. We do not know if they turn them into one of their own or their thralls aka Wights but we do know that they come with the Others:
From ACOK, Craster's wife telling Samwell Tarly:
The boy’s brothers…Craster’s sons. The white cold's rising out there,
crow. I can feel it in my bones. These poor old bones don’t lie.
They’ll be here soon, the sons.
With Books part done, according to Season 6 of the show:
Children of the Forest created first Wight using their magic to
defend against onslaught of the First Men. (But show forgets that in war against the Wights, First Men and COTF were allies). He was most likely a Captive from a battle between First Men and COTF.