Condensation doesn't occur on the outside of the window because the surface, warmed by heat from inside, is above the dew point of the outside air. On some houses, my own included, on a cold morning, you can see a pattern of moisture on the walls (insulated and cold) but also the outline of the frame without moisture(warmer due to thermal bridging).
Obviously, as mentioned, in a rental house your options are limited. Encourage your landlord to insulate by all means, perhaps there are still subsidies for him. The cheap film-glaze that you can get at hardware stores or Trade Me would be a good option as it should provide a good seal. Suggest you do a test to ensure the tape won't damage the widows on removal. Of course, try to keep the house as well aired as possible.