I’m having a debate with a friend on whether a university has the right to search mail sent to a student living in a dorm. No substances sent. If it was delivered to the school, does the school have the right to open the mail? Do they need a warrant/notify the student to open the mail?
It depends.
Shall we assume you mean mail through the postal service, not university mail?
After the Unibomber's attack at Yale in 1993, The University of Iowa informed all departments that people should be careful of unidentified packages. Oddly, the History dept. seemed to take the warning a lot more seriously than, say, the Math and Computer Science departments. I imagine Iowa State and UNI put out similar warnings, but considering the Gang Lu shooting less than 2 years before, The University of Iowa was a bit security conscious.
Frankly, I cannot imagine that anyone at a public university would give a hoot about your mail unless there was a suspicion it could cause harm.
If this is a private institution, there may be rules in the student handbook that differ from those of public institutions. When you commit to attending a private institution, you are also bound by the rules in the handbook. There may be additional rules in the paperwork for dorm rooms.