Ha. I found it. The fabric for Snow's Riding doublet is Robert Allen Diamond Tuft. Once I had the name and searched on that I realized it had come up before many times. However it was so poorly photographed that I couldn't see the pattern. It comes in both white and natural and I guess the white would work better. There is even a local place that has it.
Touchmon - I've not used that pattern but I've made many cloaks. I think they have a cape front piece so that you end up with a seam you can leave open a little so hands can stick out. One of my cloaks when spread out flat is three fourths 3/4 of a circle. The cloak back is a half circle (the fabric is wide enough for this) and the two front pieces are each a 1/8 pie piece. You may be able to cut you back piece on a fold and have one less seam to sew.