Why are the wet clothes on the balcony not easy to dry in cold and humid weather?

Drying wet clothes belongs to gasification, not evaporation. The factors that affect the evaporation rate of liquid are 1. Temperature of liquid 2. Surface area of liquid 3. The velocity of air above the liquid surface. According to what you said, the situation is 3. It's cold and humid, so it's certainly not easy to dry without ventilation. If you use a heater or an electric fan, the air conditioner will dry more easily.