The only function of the plume in battle was to identify each cohort. The horsehair would be dyed, and each color would stand for a certain unit. I do remember reading that usually during the Punic Wars, the Roman Hastati would wear very large and high plumes just to intimidate the enemy. The high plumes supposedly made the illusion of the Hastati being taller, which was somewhat true actually. A fine idea, but I am not sure how long the plume would last in battle...

The tunic and the sleeves of the legionnaire's clothing was dyed as well to color-code each cohort, or so I have read.

Oh, and yes, the battles weren't usually chaotic. Usually.