Let's limit this question to the Classical period (c. 5th-4th centuries BC)
Did Greeks harden their iron swords, spearheads, arrowheads etc. before putting them into use? Was hardening technology known for Greeks at all?
I do not know of which characteristics and quality was the steel produced for weapons and whether it was of any use for such weapons to be hardened. Probably hardening wasn't used for weapons but for other metal items.