I was pretty sure they liked wearing heavy armour.
But I could well be wrong.
Also, the Celts were awesome, with their ‘If I’ma die, no amount of armour’s gonna stop it!’ philosophy.
It wouldn’t make much sense for the Spartans to fight in the nude while wearing those cool helmets. They fought in armor. Part of the lesson of the real battle was how preparation and superior technology, which included the armor, could trounce overwhelming numbers.
The Spartans wore armor in battle (probably heavier than most since they were theoretically stronger). I think they fought naked in their military academy (the agoge) though; although that soon became an all-Greek custom as far as sports were concerned.
They wore armor. 
This is what I get for putting my balls to the walls in such a flagrant manner when I am uncertain of myself.
but I read an interview Frank Miller, which touched on that subject. He did an obsessive amount of research in making the story, but when it came time to design it he recasted basically all the historical detail. Like, if the Spartans were the world’s biggest badasses back then, it’s a lot cooler if they didn’t wear armor. So their armor isn’t steel, but their teamwork, ethos, training and the intimidation factor.