Cat
I folded this model in order to test what folding origami from felt would be like, and I summarized my impressions in a separate blog post.
Fabric-Based Folding Materials
Fabric can be used for origami, but it usually requires special treatment or sewing to keep the folds in place. Another way of making fabric suitable for folding it to glue it onto paper or some other medium, creating a composite material.
Hugging Triangles Corrugation folded from fabric
My Hugging Triangles Corrugation, executed in fabric-covered paper with aluminum foil backing (three-layer composite material).