In an Alcohol thermometer, alcohol is used as a thermometric liquid. The melting point of Alcohol is around -114$^O$C. This is less than the melting point of ice. Hence, an alcohol thermometer can measure the temperature of ice.

The boiling point of Alcohol is around 78$^O$C. This is less than the boiling point of water. Hence, an alcohol thermometer cannot measure the boiling point of water.