I've cut out the costume coat and hood. Fleece is treated like velvet, corduroy, and fur. They have nap, which means all pieces must to be cut in the same direction, or there will be different coloration in the pieces. I always cut with the nap going in the down direction. Of course, I learned this the hard way by making the mistake on a pair of slacks many years ago.
Fabric should also be steamed and not pressed, which, admittedly, I failed to do.