Quoted from Wikepedia:  "By the mid-1940s, beanies fell out of general popularity as a hat, in favor of cotton visored caps like the baseball cap. However, in the 1950s and possibly beyond, they were worn by college freshmen and various fraternity initiates as a form of mild hazing. For example, Lehigh Universityrequired freshmen to wear beanies, or "dinks", and other colleges including Franklin & Marshall, Gettysburg, Rutgers, Westminster College and others may have had similar practices.^[4] Benedictine College, in Atchison, Kansas, still carries this tradition for the first week of a freshman's classes,^[5] and is said to be the only college in the US to maintain this tradition.^[6] Wilson College continues this tradition today as a part of its Odd/Even class year "rivalry". "(https://en.wikipedia.org/wiki/Beanie_(seamed_cap) )

It seems like most colleges probably did this. The caps varied and changed from beanies:

to caps with a small brim:

Here is a story about Concordia College's freshman caps:

http://seward-concordia-neighborhood.blogspot.com/2009/05/freshman-beanies.html

and Ohio State:

https://library.osu.edu/blogs/archives/2013/08/09/long-gone-campus-traditions-hats-off-to-the-era-of-freshman-beanies/

and Brown University:

http://www.brown.edu/Administration/News_Bureau/Databases/Encyclopedia/search.php?serial=F0280