It would probably be more likely to hurt you at Pepperdine, which is a dry campus, and LMU (assuming that's the Loyola you're talking about) than at the others. Those schools are more conservative and therefore more likely to decline a student with an alcohol related write up.
Honestly this will have little to no effect on your application status. I have known people that have been arrested for DUI's, convicted of misdemeanors, and a wide number of other things. If getting drunk in a college dorm freshman year is your dark secret your doing pretty well for yourself. Realistically the only way this could possibly effect you is if you don't disclose it. However, I am only an anonymous internet poster as is anyone else on this board or others so I could be 100% wrong, but I have been found morally fit to practice law by more than one state bar so I do have a shred of credibility and I did worse things than drink as a freshman. Worry about your GPA, LSAT score, personal statement, etc and disclose this incident and you will be fine. Good luck to you.
When I was in college, I smoked pot. The first time was in Hawai'i--atUH-Manoa--in a dormitory. The second was at a house in Maine. I don't know if I was written up or not. But I did that and then got into The University of Southern Californa Law.