Personal grooming devices such as hair dryers, flat irons, curling irons, shavers, and other electrical devices, such as small fans (no larger than 12" in diameter) are allowed when in good condition and used with proper caution. Cruise lines typically provide hair dryers for you to use, so that is one less thing you have to pack.
Cruise ships generally do not allow any electrical and household appliances containing any kind of heating element, such as irons, clothes steamers, immersion heaters, heating blankets, water heaters, coffee machines, hot plates, toasters, heating pads, humidifier, etc.