My father, age 72, often complaints feeling like having ice cold drop dripped over his left lower eye lid. should i see phthalmologist or neurologist?

Either one will work: The sensation your father is experiencing may be neurological, but either type of doctor should be able to evaluate him. If this is the only symptom he has and he has no other neurological conditions, i would suggest starting off with an eye examination.

See eye MD: He could see an ophthalmologist first, and then could be referred to a neurologist if necessary.