The droplets on a glass of ice water are a result of water vapor releasing energy and changing to water droplets.

That is true.

In the solid state the molecules of water have the lowest energy content.

To pass from solid state to liquid stated water needs to gain some energy to increase vibration and motion of the molecules and reach a higher energy states.

To pass from liquid state to vapor (gaseous state) the molecules of water have to gain more energy to increase more the motion of the molecules and reach a more energetic stated.

Then you can think that when the water vapor becomes liquid (droplets) it needs to release some energy.

The droplets formed on a glass of ice water is an example of water condensation, one of the processes of the water cycle.

The droplets on the external surface of a cold glass are the result of condensation of water.

Condensation is the pass from vapor state to liquid state. As whe have stated, when water passes from vapor state to liquid state it has to release energy because liquid state is lower in energy than vapor (the molecules in water experiment slower motion than molecules of vapor).