I'm old enough to know that in Nixon's era it was commonplace for a gentleman to keep his jacket on in the office while working, even in the south where A/C was hardly universal. What you might be recalling was a photo of Nixon walking a beach wearing dress shoes. At least one photo suggested he was wearing a coat and tie as well, but close examinations cast doubt on that. But it is true that Nixon was a buttoned-up kind of man and uncomfortable in public wearing casual attire.I had assumed that when the original poster talked about wearing a jacket, he meant wearing one to work, then taking it off, to be put on again when he left or perhaps for a meeting.
I don’t recall ever working with anyone who kept his jacket on all day. I do recall that they used to make fun of Richard Nixon for doing it (not that there’s anything wrong with that).