The problem goes deeper than it looks. Opening windows helps, but if the humidity persists it's because there's serious infiltration or condensation happening. First, check whether the water's coming from outside (infiltration in the foundations, broken tile, clogged gutter) or if it's interior condensation (poor ventilation, weak insulation). Old houses usually have problems at the base - water rises up the walls through capillarity. If the walls get damp near the ground and the humidity rises to a certain height, that's it. Scrape off the peeling paint with a scraper, let the walls dry properly (it can take weeks) and then paint with anti-mold paint or silicate paint that lets the wall breathe.
If it's condensation (bathroom mirrors fogging up, mold in the corners), you need better air circulation - extractor in the kitchen, ventilation in the bedroom. Dehumidifiers help temporarily but don't solve it. The ideal thing is to create airflow, open windows on opposite sides and avoid drying clothes inside the house. If the house is too shut up in winter, you've got to take the risk - it's worse to leave it unventilated in the cold than to have permanent mold.
As for a serious solution, it's worth investigating the foundations and exterior coverings. If the leaks are actually coming from outside, no paint will fix it - you need to fix the source. Sometimes it's as simple as cleaning the gutter or fixing a tile. After that, if you decide to do a more robust treatment, there are resin injections in the walls to stop rising damp, but it's more expensive. Start with the basics: check for infiltrations, improve ventilation, let it dry and repaint with proper materials.