I have a hobby of writing video game item descriptions, usually trying to justify game mechanics within the flavor text. Elemental weapons are especially fun to explain in-universe. Lightning spears being created by people that have to fight against invaders that use full body armor, a fire sword is used by an executioner to instantly cauterize necks for indoor beheadings, that kind of thing.
At the moment, however, I'm having a hard time justifying weapons that freeze. I just can't see the advantage making an enemy's laceration, puncture, or point of blunt force trauma really really cold. Without a large battlefield advantage, freezing just seems like unnecessary overkill. They already died of the impact/wound, why are you turning the corpse into cold-cuts, you know?
Assuming that destroying or draining heat (either's fine with me. The lapse of physics can be explained with magic) from a struck or touched target requires some form of extra investment when creating the tool, why would a freezing weapon be worthwhile?
edit- I forgot to mention that I thinking of feudal era weapons and tools.