...based on the description.

This axe is quite impressive looking, with a massive twin-bladed
head, and a handle easily three or four feet in length. All along
both blades as well as the shaft are crystals of ice and frost,
spreading out to lightly cover it. Despite a great deal of wear
and tear on the axe, between nicks and dents on the blade, dried
blood encrusted on it, and the dark smoothness of the handle worn
down by use, it appears to be in excellent condition beneath the
ice. Wiping away some of the ice to test the blade, you find
it is still sharp enough to split even the smallest of hairs,
not to mention heads. Not a few seconds after the ice crystals
are wiped away, though, new ones seem to form in their place
right before your eyes.

A large battleaxe named 'frostreaver' is an axe, made of steel, and weighs 17 pounds 15 ounces.

Consensus was that if it was to be given an ice dmg that it would also gain a magic flag. So we have opted to just leave it alone.