What are you talking about? Zoro before even knowing about Breath of all things was able to cut rocks by mistake.
Rocks are more durable than Ice
Also Breath of All things is CoO not CoA
Ability to cut everything you with and nothing you don't wish is Ryou and as the name suggests, if Mihawk is using Ryou and only intends to cut flesh, it would cut nothing but flesh just like how Zoro demonstrated by not cutting the leaves yet cutting the rock.