Most likely yes when compared to men under 20 or maybe 30 years old. The available evidence suggests that young males had short hair and young females long hair, while mature males generally had long hair and married females had short hair.
In general, that would depend on the age of the man. There is some dispute as to at what age Spartan men were allowed to grow their hair long. It may have been at 20; according to D.M.MacDowell in Spartan Law, the confusion lies in the interpretation of one passage by Xenophon, but Plutarch is clear that it was at 30.
It is clear, though, that those under the age of 20 had short hair. According to Pausanius, this tradition of long hair continued until at least until 146 BC but, as Cartledge & Spawforth observe in Hellenistic and Roman Sparta,
All that remained until then of the old Spartan ways were the peculiar mode of clothing and style of hair . . . which constituted both literally and figuratively a mere keeping up of appearances.
A Spartan warrior prepares for war. Source: https://i.pinimg.com/736x/97/18/28/9718287d79c882bb7ad748405decf4d7--the-greeks-ancient-greek.jpg
Women, on the other hand, are depicted in art and literature as having long hair before marriage. For example, Anton Powell in The Shadow of Sparta, quotes Aristophanes' Lysistrata,
Let us praise Sparta, where…the girls, like ponies, leap along
by the Eurotas, raising the dust with the rapid movements of
their feet; and their hair streams out like that of maenads at
A bronze figurine of a Spartan girl runner dating from 550-540 B.C. Source: https://i.pinimg.com/736x/3e/e6/df/3ee6df287951d275ae9a26692b69787d--spartan-diet-the-spartans.jpg
When the time came for marriage (at around 18 to 20 years old, generally later than in other Greek city states), the preparation
...began with the shaving of the bride’s head; thereafter as a married
woman she had to keep it close cropped...
Source: Paul Cartledge, The Spartans
However, it is worth noting that this tradition of cutting hair short upon getting married was far from a uniquely Spartan tradition. Barbara Goff in Citizen Bacchae notes that
The bride would almost certainly dedicate her hair, an offering that
is a common sign of transition in both Greek and other cultures
Similarly, men with long hair was also not uniquely Spartan. D.M. MacDowell
...long-haired youth of Athens who associated with Sokrates.
Also worth noting is that Spartan men
were simply more conservative in the adoption of new styles, meaning
that they retained archaic fashions, such as the peplos and long hair
for men, long after Greeks from other cities had adopted new fashions.
Paul Cartledge, Sparta and Laconia
N. M. Kennel, The Gymnasium of Virtue