Would it be okay to reapply to a Ph.D. program after getting a Master's Degree elsewhere? Let’s say person A has been accepted to a Ph.D. program at Harvard, MIT and Princeton. In addition to this, he has been accepted for a one-year Master’s Degree at Oxford University. If he decides to pursue the Master’s Degree because he wants to spend a year abroad in Europe, can he reapply to the Ph.D. programs he turned down?

How would an admissions committee react to this, given that the very same applicant applies one year after having been accepted, but didn’t accept the original admissions offer?

Note, that there are very similar question on stackexchange already. But they didn't ask for the situation I have described above.
I think you should ask the three schools in the U.S. that offered you a spot.  But don't tell them the reason you shared with us for why you want to go to Oxford for a master's.  Just say it's an exciting opportunity.  

Ask whether you can defer your admission for a year or whether you should reapply.  If they say you should reapply, then do so.