I trained in massage as a hobby 42 years ago and taught it to friends. I have been massaged by men and women, including situations where I was offered a "happy ending". I have never seen massage as particularly erotic but it is sensual (and caring/loving with some people), so I have never accepted a happy ending.and only once many many years ago a friend asked for a handjob and I did.
I prefer to be massaged nude and undraped but not a strong preference. If a masseur/masseuse wants to drape me that's fine. If the room is not warm enough to be comfortable with uncovered oiled skin then it is important to cover the body, other than the part you are working on, with a warm towel or towels.