That might make sense in some situations. If they were naked and oiled up it would be very difficult for an opponent to grab hold of them. (Ladies, please restrain yourselves at the mental imagies ). I know the fights that were held in the original Olympics involved the contestants stripping and oiling themselves, so they might have brought this into warfair or taken it from their battles.
It would also mean that clothing wouldn't be forced into a wound and cause an infection-some duelists in the 17-1800's would fight bare chested so if they were hit their clothing wasn't forced into the wound. Given that most of the wounds in a Greek era battle are likely to have been from penatrating wounds (from spears and arrows), rather than from cuts from swords this would make sense.
It could also be that the Spartian armies were meant to move quickly, in which case dropping some of the armour would make sense. The Hopilite/Phalanx formation was intended largely for only short distance warfair-defending homes for the most part-not for treking long distances. Spartans might have left everything but their weapons at home if they needed to be somewhere very quickly. And if that meant they were wearing no armour they might as well have got rid of the clothing before battle as it would have made little difference to the way they could fight. (The Spartans at Thermopylae might have been sent there was quickly as possible, in which case they might have left as much heavy equipment as they could at home so they could move as quickly as possible).
Then fighting naked could have been a way for the Spartans to show that they were not afraid of an opponent-'Look, we are so brave/powerful/fearless we don't need armour' or just a way to scare the opposition. The Celts used to fight naked as well to frighten enemies and for the warriors to show their bravery.
But Mandalorians aren't the kind to retreat, as in dropping their armour and fleeing, they wear heavy armour, so they don't fight naked either. That is the Echani (sort of)
The only thing is the red robe that Mandalore is depicted wearing in the comic. But is that canon? *shudder*
The Mongols wore silk so the arrow was easier to remove.