I think you can not.
e.g. in Solidworks linear dimension has one color, either it is all red or all black or whatever it is not split in text color and dim lines . I think you have to do on the Autocad side, you could possibly do it with AutoLISP, either find one to do it or make one.
hope this helps.
You have to set it in Autocad in Dimension Style Manager.
For example you can set the Lines ans Arrows color "ByLayer" and set Text color to any color you want. That way your dimension lines will be same color as layer and text in the color you chose.
I really miss that in Solidworks.