Does the idiom 高城深池 have a positive or negative connotation? The dictionary says that this idiom means impenetrable defense (high city walls, deep moat). Does this mean that an individual described with this idiom is stubborn or strong in resolve?
It is a neutral term. It describes a property of an object. Not commonly used in a metaphorical sense to describe a human characteristic
高城深池 is typically used to describe a defended city, base and of course, castle.
There are many idioms graphically describe objects with no metaphorical usage.
Example:
一望無際 (cannot see the edge) describe the view of a vast area - express: vastness
皮堅肉厚 (tough skin and thick muscle) literally describes a man or an animal with tough skin and thick muscle  - express: physically durable
水清山秀 (clear water and beautiful mountains) literally describes a place with clear water and beautiful mountains  - express: beautiful scenery
高城深池 literally describes a castle has high wall and deep moat - express: impenetrable defense