Droplets form (or, if you prefer, condense) when the cooler glass reduces the temperature of surrounding air enough that the air becomes oversaturated (contains more than it can hold) with water vapor. The extra water vapor then forms liquid water as droplets on the glass. The temperature at which the air is holding just as much water as it can is called the dew point. However, this is not a set temperature because the amount of water that air can hold will change with temperature; warm air can hold more water than cold air. This is also related to the relative humidity that you might see in a weather report, and knowing the temperature and %relative humidity allows you to estimate the dew point .

Droplets appear on the glass surface because water molecules condense from the air. In order for condensation to happen, the temperature of the glass should be lower than the dew point of air. There are two things that affect the dew point of air: relative humidity (the amount of water vapor in the air) and air temperature. You can check out this website (also in previous answer) for calculating the dew point: www.dpcalc.org.

Let me give you an example. Weather determines relative humidity. In Santa Barbara, the average daily relative humidity is 71%. Let's assume a comfortable room temperature of 77°F. The dew point at these conditions is 67°F. What does this mean? This means that as long as you can make the temperature of the glass lower than 67°F, then droplets should appear.

Filling the glass with ice should reduce the glass temperature to somewhere around 32°F, making condensation possible. In fact, assuming an average relative humidity of 71%, an ice-filled glass should have droplets form on its surface as long as the air temperature is above 41°F.

It has nothing to do with the temperature of the glass. In fact, the temperature of the glass is the always same, zero degrees Centigrade, because that is the only temperature where the water in the glass can be liquid and the ice in the glass will be solid.

What it does have to do with is the humidity of the air outside of the glass. Warm air can hold more water vapor than cold air, and when warm air touches the colder glass, the air cools off. If this leaves the air too cold to hold the water vapor that is in it, then the excess water vapor will condense into droplets on the glass. You can see this very easily if you do this experiment in a wet climate versus a dry climate, because the air in wet climates tends to be humid.