No, they have a native hardness modified by the hardness field. If the ore has a natural hardness of 15, and the field is, say... 2.0*, you'll need to be able to mine a rock with hardness of 30. To figure out what hardness you can mine, take the square root of the product of your tool (stone axe or pick axe) and strength. (In case you're curious, this is called the geometric mean, and is used a lot in quality calculations in Haven.)
*I'm pulling these numbers out of thin air. I've no idea how the server tracks things internally, but I think it's a decent representation of how things generally work by the way it was described and previous knowledge.