I do not recall seeing any hoodie with a silkscreened or embroidered logo that was not cotton.
I do not wear a cotton for cold weather camping/outdoor wear. Cotton is fine for just puttering around the yard or shop. Not good for outdoor activities.
Cotton loses its insulating value when it gets wet, or even slightly damp. In fact, it becomes a negative insulator, or conductor, making you colder (which is why it feels comfortable on a hot summer day). My cold weather outdoor wear is synthetic fleece that retains insulating properties even soaking wet. A bit pricey, but well worth it. A quality brand name will last a lot longer than an inexpensive cotton hoodie.