Fleece in a dream signifies the feeling of warmth and protection. It also might represent a sense of security.
A good example is when you are dreaming about watching a movie from your couch, surrounded by fleece blankets. Or someone was using fleece to keep themselves warm while they were outside in the cold weather.
Wrapping yourself with fleece in a dream might also signify those who have been assigned guardians, such as foster parents or nannies.
The person who is wearing the fleece may feel protected and secure, even if it is not physically true. They may still feel that way because they remember times spent with their guardian where they felt safe and secure. Fleece often symbolizes this type of warm relationship between two people who care for one another deeply.