Perhaps in the context of what the OP was originally trying to do only.
However, I was doing a search and came across this post because I’m needing something similar.
I’m needing to have dimensions on the same layer as my objects but being able to assign a unique color per dimension per layer.
This helps differentiate an object line from a dimension line, and also helps know at a glance which dimensions belong to which layer and which objects.
Not being able to do this actually turns it into many steps and many additional layers.
I was looking under properties tab with 'Linear Dimension" selected. And there is no color property/settings for it.
But if I select “Object” it does let me set the color other than layer color specifically for that dimension.
So the problem really was my assuming a Dimension is a dimension only and not an object - like what we create( ie. information about an object, not an object itself). I think otherwise I would have looked elsewhere. Now I know Rhino has an ‘expanded’ definition of what an object is.