Don't ask them about stats you could easily find online. Rather, ask questions that demonstrate you've 1) researched the program and 2) believe it is a fit, based on that research. Use that as your jumping-off point for deeper conversations. Initiate as many meaningful conversations as possible, without sacrificing quality.
After each conversation, take their business card, and write down what you discussed.  Within 24 hours, email your new contact to follow up, the same way you would send a thank you note after an interview. It's helpful to reference what was discussed, to reinforce the connection and make you more memorable. You can also ask them to set you up with a student mentor, and if possible, have them arrange a school visit. This will win  a lot of points. Keep in mind, showing a specific interest in a school will up your chances.
The biggest headache for schools is extending offers to people who choose another school. In this way, it's a prisoner's dilemma. So doing the work to demonstrate that you would pick them will impact your chances.Â
You can get even more mileage out of each event by noting a meaningful piece of information in your essay; i.e., I spoke with Flor ('12) at the Buenos Aires admissions event, and she mentioned XYZ about Cornell. XYZ = something that would make me a fit at your school.
And please don't mention collaborative culture because 99.99% of applicants go that route. It is played out.
If you do mention it, show don't tell - mention a clear example of what resonated with you. If possible, reference an alumni conversation in your essay that points to how the school is an especially strong fit with your unique career goals. This is a good idea for the prisoner's dilemma mentioned above.
If you are unable to attend any events in person, make sure to subscribe to their You Tube and attend the online admissions events. Meet with students or alumni in your city; get creative to show the school you are passionate about their program!
In sum: make a good impression - before and after the event!
