What about This restaurant owner is cold. Or This restaurant owner is not affectionate. I don't see where person or very are.
I think you're trying to directly translate. A more common English equivalent to this sentence is, "The owner is a very cold person," as in distant and non-welcoming. Since you can't directly translate the word "cold" into a Korean word with the same meaning, the mods have used different Korean words instead to convey a similar meaning.
Also, "This restaurant owner is not affectionate." is accepted now. I just used it on Aug.3.2018
This is and will be a problem when translating Korean into English. 정이 없어요 is very context dependent and can be rendered in English in many ways. All correct. Is cold. Is very cold. Is a cold person would all be considered correct. If you want to be more precise, the focus however is not on what kind of person he or she is but on his or her attitude/behavior.