"Musty" sounds bad, "woodsy" sounds good. Boat makers solve this issue by ventilating storage areas. It sounds as if your nose is sensitive to the smell your trailer emanates. My trailer has a distinct odor that stored fabrics pick up. It comes from adhesives, finishes and laminates used in construction. IMHO, it will be a loooong time before your trailer goes "neutral."
Solution? 1) Live with it and don't be concerned. 2) Substitute a smell you can tolerate with scented oils, sprays (such as Febreeze) or other similar product.
Wright and Penny
2010 Tundra 4X4 5.7L V8
2014 Rockwood 2604WS
Life is a cruel teacher. She gives the test first; the lesson then follows.