I guess vacuuming off the hair and any loose dirt would be step one. Then perhaps spot cleaning any ‘incident’ areas with a pet-safe detergent? Remember not to overdo with water as…well…it’s still wool at end of the day even though it’s synthetic. Just my two cents here from my experience in handling fuzzy fabrics (beaten by sweaters in life more than once!). Have anyone tried this method with their Ugg bed?