There are two factors in play. One is the temperature gradient between inside and outside and the other is ventilation/air movement. A fitted wardrobe in itself is insulation - it is between the warm fairly humid room air and the freezing temperature outside. Any internal insulation will move the dew point of that temperature gradient inwards. The dew point of ambient air (say 20-22 degrees and 50-60% humidity) is around 12-13 degrees. If the room air hits a surface at the dewpoint temperature it condenses. In a room where there is a fitted wardrobe on an outside wall, the wall is protected from room heating, so is colder - the insulation provided by the wardrobe has moved the dewpoint inwards so instead of being inside the wall where it would be if the wardrobe wasn't there, it is closer or even on the wall surface.
If any of that room air is moving passed the condense, as it is only at 50-60% humidity, it has the capacity to evaporate any condensation away - hence the reason ventilation is so important - there can be an equilibrium where the evaporation is equal to teh rate of condensation - as long as the rate of evaporation can be greater, the moving air has a drying effect - the faster that evaporating air is replenished the faster the drying (hence drying clothes on a windy day is better than a still day). In a situation where there is no air movement, the condensation occurs but doesn't evaporate - the still air immediately above the liquid water becomes 100% saturated because it can't move away and the liquid condense persists.
Liquid water = mould
So the answer to the question is 1) yes, insulate an exterior wall if you can - it will move the dew point inwards, but hopefully behind the wall surface where the room air can't get to it and condense. The idea is that the insulated surface is above the dew point because it is in better contact with the room air and hence warmer 2) Try and get air movement in to the room - open the windows in the day time. Ventilation is the no1 remedy for condensation and damp.
If all else fails, use a dehumidifier to lower the humidity of the room, which has the effect of lowering the dew point, hopefully below the surface temperature of the surface of the external wall behind the wardrobe.
