You're right Vanya, the tradition of female warriors seems to have been found among mortals rather than elves, at least as far as the Silmarillion tells us.
Actually it wasn't just Haleth, among the Haladrim it was a general custom for women to fight.
Morwen did not fight, but her female relative, Beren's mother, Emeldir the man-hearted, did.
As for elfwomen - in UT, Galadriel fought to defend Alqualonde, and in many versions of the Fall of Gondolin, Idril Celebrindal donned armour and fought.
But that's about it.
However, Tolkien also has the following to say in Morgoth's Ring:
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There are, however, no matters which among the Eldar only a ner [male] can think or do, or others with which only a nis [female] is concerned.
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Also:
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Indeed in dire straits or desperate defence, the nissi [females] fought valiantly, and there was less difference in strength and speed between elven-men and elven-women that had not borne child than is seen among mortals.
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Howeve, he seems to be specific about mothers not fighting, and that healers of either sex should not go to war.
Actually your question has set me wondering about how elven women did pass the time. Not on childcare - they lived for thousands of years, most of them only had a couple of kids in that time, and they, says Tolkien " needed little governing or teaching. "
So what were they doing? Weaving? Playing on dulcimers? Having pedicures?