Currently playing a Brawler in a campaign where demons are a common enemy and I'd like to use cold iron gauntlets to overcome damage resistance using my brawler's unarmed strikes. However, I've read on another question that using gauntlets like this merely lets you augment your unarmed strikes to deal lethal and that enchantments (i.e. +1 enhancements) only work if you are using the gauntlets as a weapon. Is this also the case when they're made of a material that is for overcoming DR?
The rules for gauntlets are a mess. They’re a perennial source of confusion, we have a whole bunch of questions about them, and there are just no good answers. Instead, you get the sort of answer that goes “well, you see, it says this and that and the other thing and they are vague and maybe contradictory and we just don’t really know.” And there can be some value in that; laying out all the details and letting readers decide is generally a good choice for ambiguous situations. I’ve written several answers like that on this subject myself. MikeQ’s answer is another in that vein, getting into why it’s so messed up and problematic.
I’m going to try something different:
Yes, of course they should!
Unarmed strikes are awkward, difficult weapons to use. They are nothing like high-power options. So eliminate as many of the potential stupid limitations on them as you can. Let brawlers and monks use cold iron gauntlets if they want or need to. It just makes the game better. Deciding to disallow it just makes the game worse.
So regardless of how the rules mess shakes out, the answer itself can be clear: the correct answer for the best gameplay is simply yes.
The gauntlet material probably would not affect the unarmed strikes.
Gauntlets and unarmed strikes interact in funny ways in Pathfinder. The gauntlet weapon description arguably suggests that gauntlet attacks are unarmed attacks without being unarmed strikes. But gauntlets are manufactured weapons whereas unarmed strikes are not, so the they are considered different types of weapons. Proficiency, feats, or other features that affect one do not automatically affect the other.
The Brawler's class features that explicitly boost their unarmed strikes only boost their unarmed strikes. They get other features (like Close Weapon Mastery) to boost their attacks with gauntlets and similar weapons, and those attacks get different benefits.
By RAW, when a Brawler makes an unarmed attack roll, they apply relevant feats and features that explicitly modify their unarmed strikes. So the Brawler's fists could be covered in cold iron, or adamantine, or cloth, or thick wool, or nothing, and the attack and damage rolls of the unarmed strikes are handled the same way.
However, Wondrous Items are the exception here. Certain Wondrous Items (such as the Amulet of Mighty Fists) expressly modify the Brawler's unarmed strikes. Some of these Wondrous Items have "gauntlet" in the name, but they are not considered as gauntlet weapons.
Should the material modify your unarmed strikes this way?
Unless you're following organized play rules (such as Pathfinder Society), ultimately the players and GM can decide the rules for your game. So even if the RAW doesn't really support it, the GM could allow it for the sake of fun and simplicity.
Letting a Brawler overcome DR/cold iron by equipping cold iron gauntlets would be a very small advantage compared to other Brawlers of their level, but not an advantage significant enough to unbalance the game.
Brawler's unarmed strikes will bypass DR/cold iron at 9th level, as part of their Brawler's Strike class feature. Letting them bypass DR/cold iron with mundane gauntlets would effectively grant the benefit of a 9th level class ability.
On the other hand, Brawlers are a specialized martial class (compared to the spellcasters who can easily adapt to enemies with DR, flying, incorporeal, etc.), so it's reasonable to argue that an item to bypass DR/cold iron is such a small benefit that it would not disrupt the inter-party balance.