No. The walls of the room are still my property. I do allow them to decorate their furniture (dresser and bed) with stickers though. I don't want them in the habit of coloring on walls and taught them that paper (which includes any of the recycleables in the bin that they can turn into art) is the only thing that can be colored on, so it would be pretty confusing for them if I told them it was ok to color on their walls as well.
They can have any input they want on the decorations in their room though--they help pick out paint colors, bedding, wall art, curtains, etc. But I wouldn't let them dye my carpet in their room and I don't let them draw on their walls (unless I hang a big sheet of paper up first). They aren't old enough to paint the walls to cover it up with they're bored with their scribbles and I'm certainly not repainting the room every week when they want a fresh pallette.
: So, they can color on paper.