Rules as written, they can wear metal armor
The Witchbreed package for Golems has two parts that are relevant to this:
Constructed: While a Golem’s soul is that of a mortal human, his body is a construct of stone, steel, straw, reclaimed flesh, or some other material. Golems do not suffer from disease or poison. They do not suffer extra damage from called shots, nor do they suffer penalties from Wound Modifiers. In addition, they add +2 when attempting to recover from being Shaken. Golems cannot heal damage like their mortal companions. To heal a Golem, a character must use the Repair skill instead of the Heal skill.
The choice of being constructed from stone, metal, or some other material is purely aesthetic, since all Golems have the same stats regardless of the material chosen. Furthermore, nothing says that armor made of metal, wood, cotton, human flesh, or anything else is in any way affected by the material chosen.
Hulking: Golems are, on average, taller, broader, and stronger than other Accursed or the average mortal. They gain a +2 Toughness modifier thanks to the sheer mass of their constructed bodies, and the reinforcing elements added to them.
Golems do gain +2 Toughness due to the material they are made of. But even so, this is Toughness which is different than Armor that chainmail or whatever provides. While Armor does not stack with other Armor, it does provide protection in addition to Toughness.
In other words, when someone tries to damage you, their damage must exceed Toughness + Armor (although usually stat blocks write it as something like Toughness: 8 (2), which in this case would mean 2 points of Armor, thus "innate" Toughness is 8-2=6). Toughness is usually calculated by ½ Vigor+2, but your Golem adds +2 on top of that. The can still add +Armor on top of that.
To give a concrete example, Humans would have a Toughness of ½ Vigor+2. Golems get a +2 on top of that. So if my Golem has a d6 Toughness, his Toughness is ½(6)+2+2 = 7. If I give him Chainmail (+2 Armor), an attacker must deal 9 points of damage or more to harm the Golem (and a statblock would write it as Toughness: 9 (2).
Using the English version of the original Kickstarter rules.