This misconception is even found in some textbooks. The speeds of water molecules determine condensation and evaporation rates. All molecules are moving, even in ice and other solids, such as steel.
Molecules move much more rapidly in gaseous state than in a solid.
Water molecules vibrate back and forth in a block of ice, but move randomly in the liquid and gas states. The speed of each water molecule determines that molecule's phase - gas, liquid or solid. Evaporation and condensation both occur at all temperatures. The temperature of the air, the water vapor in the air, and the surface of liquid water determine whether condensation or evaporation dominates. Suppose we have a parcel of air in which condensation and evaporation are equal.