I'm a little confused, why would you be sewing a 1/2" seam through 4 layers of fabric vs. 2?
You could make a rag quilt using fleece, the ends don't "rag", rather they "fringe" and the effect is pretty nice. Good directions for making a rag quilt are here -
http://greenappleorchard.blogspot.co...-tutorial.html Fleece does tend to be heavy when you are sewing together 2 pieces front and back, so leave out the middle piece you would generally put between the individual blocks when using flannel or cotton. I've made lots of rag quilts using fleece, with just one layer of fleece and with 2 layers.
Here's pictures of a couple I've made
http://www.quiltingboard.com/picture...lt-t76618.html
You can also just do a block quilt. Cut your snowman squares, sew them together with your bright squares, then put the backing on and stitch in the ditch to join the two sides. Or quilt it. If you want to do binding, I recommend cutting a larger backer and bringing the edges over as binding, it's a little easier to work with. The instructions for that technique are here
http://www.lorettaalvarado.com/binding.htm