I did a bunch of MSTP interviews last year and this year I'm heavily involved with hosting applicants - just so there is no confusion:
There is no real alternative to suit (the coat may be optional, but otherwise no) during the day(s) of the formal interviews. While many schools will have you meet with research faculty of your choice informally as a part of the visit, in reality, those also tend to happen on the days you have your actual interviews, so the technicalities of changing back and forth usually dictate that everyone is just wearing their suits during the day.
The exception to this would be any informal interviews during your second look weekend, once you're already in.
What I was referring to earlier was the fact that it looks bad when you go to the student dinner at night, or out for a drink or whereever the students are taking you (we take people to a dinner and then, depending on how late it is, etc., to some more relaxing place), you're still wearing a full suit.
Now this has happened, but it has ususally been accompanied by the students bitching about not having time to change, and that's fine. People who are overall anal usually stick out no matter what they wear (having said that, don't wear a bowtie to your interviews, people, as some have....)
As far as the students having a say in admissions, it differs heavily from school to school. I promise at Yale, we don't.
There are schools that actually have a formal interview with a student (MD at Yale, sometimes), and then that matters, but under no circumstances are these the same students that take you out and hang out with you. The idea, at most schools, is that the student events should truly be a forum where you can be yourself and relax and say and ask about how it really is - without a fear of negative consequences. Now, I can also tell you that we are all very close with our administrators/directors, so if someone does something ridiculous, we would tell them.
There was a school where my student host admitted to me, after I was accepted, that her director invited her for a talk after having hosted me, and asked her what she thought about me. This is very rare, and I guarantee it doesn't happen at many schools, definitely not at Yale.
However, beeing unusually cool will certainly get you some unofficial brownie points.