With fleeces, the material is thicker, therefore requiring a substantial improvement in the digitization of the logo.
The threads are designed to be thicker and fluffier, and the underlay is also changed from normal. In this video/blog post you can see the logo from Alexanderman Imobiliare from Suceava being embroidered on the back. It looks a bit dark in the video, but as an example I think you can get the idea.