We run a dehumidifier. We have wintered in our RV several winters - in Monterey, it was cold, damp and there was so much condensation that our mattress eventually molded out. After we all got sick (we didn't know our mattress was moldy until we got sick), we decided it wasn't worth the risk. We keep the RV at about 40% or 50% humidity- we run the dehumidifier only at night.
Anything you use that burns propane also puts out water vapor - so stove/oven, furnace and water heater. Also - your breathing - especially at night will put out a fair amount of moisture.
Pull the mattress away from the wall, leave a vent cracked (use a max-air type cover for rainy days) and if that doesn't help with the humidity a dehumidifier should do the trick. We bought a "quiet" model. It isn't terribly quiet, but not terribly loud either - and we don't run it in the bedroom - we run it in the living room. You could also run a fan into the headboard area while you sleep if it won't make you nuts. The dehumidifier also adds a small amount of heat to the space - which is nice when it is chilly outside.