A few searches here at the forums and also at the Nexus forums didn't show much result, so I'm assuming this hadn't been asked before. Correct me if I am wrong.

Right to the point - I am creating a follower, and I do not want him to take his initial armor off. EVER.
The follower has a specific type of headgear that replaces the head, and I need this to stay on the follower.
If the player gives him any sort of helmet with better stats, he will replace the headgear originally given to him.

Any help would be appreciated.

I'm not sure how you would do it, but could you not just stop them being able to trade items like when you first meet Serana in dawnguard, so the player cannot trade items, they just reject their offer? - you could look at Serana to see if there is anything there as well that would help you with this or maybe look at the quest dialogue or something?

Define a property headhelm for the piece of equipment you don't want your follower to be able to get rid and insert a line in The Oninit event of the follower's attached script: EquipItem(HeadHelm, True, True) Now, don't allow accessing it's inventory or if you want, make the item unplayable, so the player won't be able to take it out.

Of course, the player could use use some console commands that would make your follower unequip or even lost the helm. To avoid it in most cases, add this event to the script:

Event OnObjectUnequipped(Form akBaseObject, ObjectReference akReference)  if akBaseObject = HeadHelm    EquipItem(HeadHelm, True, True)  endIfendEvent

That worked like a charm, amgepo. Thank you very much.