So by default, each ash of war has an affinity associated with it (standard, keen, heavy, poison, whatever). Through the game you collect key items called whetblades, that allow most ashes of war to take different affinities than normal. Like, that soldier camp at the start of the game has the iron whetblade, which allows most ashes to add standard, keen, or heavy affinities. You collect other whetblades later that unlock other affinities. Each affinity changes the scaling on the weapon. Heavy skews it toward Strength, Keen toward Dexterity, etc. The Magic and Cold affinities change the damage typing of any weapon to part physical and part magic, and adds Intelligence scaling. Cold affinity adds less damage but also gives the Frostbite effect, which is super cool. So you can find an ash of war effect you like, add it to any qualified weapon, and if you have the appropriate whetblade you can change the affinity to Magic or Cold to give it partial Intelligence scaling. I spent much of the game using a staff in one hand and a Bloodhound Step Cold-Affinity Urumi in the other, for two int weapons and what used to be a really overpowered ash of war.