Rules as Written

It may seem that way, but the ability further clarifies how it works:

Cold (Ex)


  An ice golem's body generates intense cold, dealing 1d6 points of
  damage with its touch. Creatures attacking an ice golem with unarmed
  strikes or natural weapons take this same cold damage each time one of
  their attacks hits.


So two things happen because of this ability:


The golem slam attacks deal an additional 1d6 cold damage, that can be seen on his stat block: 


  Melee 2 slams +9 (1d6+3 plus 1d6 cold)

And the ability specifies that anyone attacking the golem with unarmed or natural attacks will take 1d6 cold damage. If it also worked against grapple attempts with barehands, it should specify so.


If a simple touch would also cause that damage, the ability would make that clear, because it would also affect casters trying to deliver touch spells.
As written, all rules must be clear how an ability should work or not, anything that isn't clear is left for each GM to decide, which brings us to...

Rules as Intended

Though the ability's wording is clear that simply touching it shouldnt cause the extra damage to you, that is clearly not how it is intended to work. But i simply believe nobody asked themselves What would happen if someone tried to grapple this guy? during the development process.

A fine example of that are Fire Elementals and their Burn ability. What should happen when you hug a big ball of flames? You should hurt yourself in the process, and most likely catch on fire.

Personally, this is how i would rule it on my table.


  If a Golem were to initiate a grapple, would this ability trigger
  dealing damage to grappled target?


Now, if a fire elemental or ice golem initiated a grapple, RaW it wouldnt deal an extra damage, because you can attack the grappled target with a unarmed, natural weapon or light/1handed weapon, that should deal the ice damage.
But RaI, it would be really nasty to get your arm/leg freeze while being punched in the face by ice blocks. Golems hardly would initiate a grapple due to their intelligence score, but i could see a fire elemental doing so to bring a burning death to their foes.


  If so, would this be on the Golem's turn, on the target's turn, or on
  both turns?


On the golem's turn if he initiated the grapple, on the grappler's turn if the golem is grappled.

Interaction of the Cold extraordinary ability and Grapples
I have seen several builds on OS 4.3 and 4.4-- what are the key differences? I tried finding documentation on the exact changes, but couldn't find any.

I set up two new Nexus 7 tablets (2013) and even brand new ones come with different build versions.
