1) Simple phobia 
Cryophobia: An abnormal and persistent fear of cold, including cold weather and cold objects. Sufferers from cryophobia experience anxiety even though they realize their fear is irrational. To avoid cold, they may live in a warm climate, dress more warmly than necessary, stay indoors on cold days, and avoid cold foods and ice cubes. 'Cryophobia' is...
Cryophobia is the fear of ice.
[n] - a morbid fear of freezing
cryophobia 1. A hatred, or fear, of being cold. 2. Unable to exist in cold temperatures.3. An excessive fear of cold, ice, or frost.
noun a morbid fear of freezing