I'm not entirely sure what you mean by "the" Christmas Tree pattern but I think any motif/image/quilt block could be adapted to make an attractive throw quilt. This
sunflower block, for example, uses a number of different fabrics to make up the sunflower shape - you could just increase the size of the pieces to make a large sunflower quilt. You could also pixellate an image with small pieces like you would a cross-stitch pattern...
I can't say I've done this - I'm just imagining what you could do. :-)
Edit: Okay, I just re-read your post and you were talking about a rag quilt. I don't think the pixellation idea would work but I think you could get the sunflower or another flower idea to work if you piece the brown center as well... Again, I've never made a rag quilt so I'm just in the world of my imagination. :-)
Good luck!