The answer from @nielsnielsen is a good start. I would add that in some extreme cases, a de-humidifier might also help. Read about the topic on the net.
However, the air humidity itself is not the biggest issue. The biggest issue is that the humidity in the air (the vapors) condensate on cold surfaces, and that condensated water is the ideal environment for the mold to grow.
Especially taking into account that the mold is on / near the windows, the problem tends to be quite obvious. Either you need some adjustments to your windows, or you need new windows entirely.
Why? Because the low temperature from the outside penetrates "completely" into the room, allowing the vapors to condensate. Either:
- the surfaces of the windows do not match properly, and air can travel freely between them,
- or the lifetime of the windows reached an end and they need to be replaced.
Either way, a specialist should be consulted, for the best advice on the topic of windows.
One extra note: make sure that the air can circulate freely in the affected areas. In this way, the condensated water has a chance to evaporate again, before mold will appear. Try any (all) of the following:
- remove any furniture which is too close to / around / above the windows;
- remove any curtains / drapes / anything which separates the room from the windows;
- remove live plants from near / around / in front of the window.
One extra help in thermal insulating your apartment is to add external window blinds. They will create an extra layer of air (insulation), which will keep the cold outside. Of course, they will have to stay open during the day, but the biggest trouble is during the night, when the temperatures are lower.
Other hints (brainstorming, you need to decide depending on your exact details):
- do not dry clothes in the affected rooms;
- do not have too many plants; they evaporate the water that they not need;
- install a kitchen hood; make sure that the vapors go outside, instead of being recirculated inside;
- install proper air exhausts (ventilators) in the bathrooms; the air with vapors must be moved outside, instead of pushed inside the rest of the apartment;
- refresh the air inside the apartment more when it is dry outside;
- refresh the air inside the apartment less when it is wet (rainy) outside;