Asking for a site visit as a master's applicant
This is totally appropriate and a great idea.

Simply send an email to the contact person (who may have a title like "graduate coordinator" or "graduate chair").  


  My name is Edna Farblefester and I'm a junior at the University of Southern North Dakota at Hoople.  I am interested in applying to your program next year.  I will be in Amsterdam next week and was wondering if I might be able to meet with you or some of your colleagues to learn more about the program and some of the faculty's research.


They should certainly say yes unless there are some extenuating circumstances.  Graduate programs are always eager to recruit students, especially in a case like this where it costs them nothing.  They probably do these sort of meetings all the time, so it should not be much of an inconvenience for them, even on short notice.

They may also offer to set up a campus tour, arrange a meeting with one or more current grad students (very useful), and provide some information about living in Amsterdam.

If there are one or two professors whose research particularly interests you, you could send similar emails to them directly.  (Mention that you are already getting in touch with the contact person, otherwise they will probably suggest that you do so.)

One final note: your phrasing "asking for a site visit" suggested at first that you were going to ask them to pay for the costs of your trip, which would be sort of an unreasonable request (it would be for them to offer if they wanted).  Of course, that isn't what you meant, but you might just want to check your phrasing when you write your email.