I have died a lot of sawdust with Rit Dye. It works and I have not noticed that mine faded. I did sift the sawdust to get mostly fine stuff. And I did glue it down with white glue and water in a 50-50 mix.
Lately I have been using ground foam on a friends layout and I think I likeit better than the sawdust. I can get more diverse sizes and shapes.
I also tried using static grass type stuff without the electrostate applicator. I did not like it. It looked like a coating of short thin hairs. More like ground felt than foilage.
Try different things and see what appeals to you.