http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Coma.html
"At a later time the Spartans abandoned this ancient custom, and wore their hair short, and hence some writers erroneously attribute this practice to an earlier period (Paus. VII.14 §2; Philostr. Vit. Apoll. III.15 p106, ed. Olear.; Plut. Alc. 23)."
And before that, Spartans had short hair util they reach adulthood and finish mandatory training- that was around 21 yr old. As for Plutarch and Herodotus, they are to be taken with a grain of salt, because they've made plenty of outrageous claims and descriptions.
http://spartareconsidered.blogspot.com/2011/09/physical-appearance-of-spartans.html
"In addition to these sources, the admittedly dubious Plutarch claims Spartan men took particular care of their hair especially in the face of danger and refers to an alleged quote from Lycurgus that long hair was preferred because it rendered a handsome man better looking, and an ugly one more frightening.
Whether the locks depicted in ancient sculpture were in fact braided or plaited is not possible to tell from the stylized nature of the evidence. However, it is physically impossible to keep long hair in neat, orderly strands when engaged in sports and other strenuous activities unless it is carefully confined in some way. Thus, practical modern experience suggests that Spartan men did braid their hair, something that is consistent with – though not definitely proved -- by the archeological evidence."