Before you get a damp surveyor in (aka salesman!) - you need to figure out a few things. The clue is in your bedroom being the coldest room in the house. Cold = condensation, because you sleep and therefore breathe in there, which produces moisture, which in a cupboard has nowhere to go. Is there anyway of warming your bedroom up and also ventilating it? Is the rest of your bedroom dry? Can you have ventilation for your cupboard by replacing the door with a louvred one? I lived for 2 years in Auckland, which has a very humid climate, and my shoes and all leather went mouldy! Mould is dangerous to breathe in, so if you can, you need to remove the mould in the cupboard with a mild solution of bleach and water, or fresh lemon juice diluted with water. And then ventilate the cupboard and the room, and try and get the room warmer. If this is not possible, you can buy small dehumidifier which should dry the air a bit and keep your cupboard dryer. Failing all that, then call in the damp boys!