I think you will also find that once your place gets hold of a mould, it can then become quite difficult to erradicate it completly as the mould is like weeds in a lawn, which you can fight and appears to come back again and again, so i would say you will need to treat and seal all your walls so that any existing pores (mould pores) are sealed and any that may have found its way into small crevices and behind furniture needs to be tackled so that it does not seed up and grow again even when the conditions of damp or moist air has improved through providing extra ventilation/.
Using oil based paints can seal the walls covered in mould, after which you could apply the normal emulsion based paints, using strong chlorine based bleech kills the pores and so use plenty of it to neuteralise areas that cannot be painted, such as the furniture, and synthetic carpets can be bleeched without loosing colour, but always test a small area first. Bleech works great in killing mould, but there are probably other dedicated agents that you can use, of course you may not be able to bleech everything, or some people just don't get on with bleech.
If you could also open the room windows for say half hour, even in real cold winter days, atleast that will allow you to remove moist laden air in your rooms and after which you can close the windows and resume the warmth, in half hour your room will not get that cold if you open the windows fully just to went off stale air, the warmth will return soon, but keep the heating on.
I don't know if you may have noticed when mopping tiled floors, the floor dries slow even if the room is really warm, but dries faster when you have a flow of air over the floor even if it is real cold air, so opening room doors and windows for a brief time will remove more moisture than an air brick.
