The answer is chapped. Milady's shave-guideline list states directly: do not use hot towels on skin that is chapped, blistered, thin, or sensitive.
Freckled, tanned, and wrinkled skin aren't flagged as reasons to skip hot towels anywhere in this guideline — they're cosmetic or age-related characteristics, not skin conditions that make heat risky. Chapped, blistered, thin, and sensitive skin, by contrast, are all genuine heat-sensitivity concerns the book calls out together.
Milady Standard Barbering, 6th ed., Ch. 13 (Shaving and Facial-Hair Design), p. 339: "Do not use hot towels on skin that is chapped, blistered, thin, or sensitive."
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