Yes you can walk onto their campus while openly carrying your firearm, but unfortunately, they can have you removed from their campus for doing so. Do they really have authority to do this since they are state owned? No, but our state legislature has granted them that authority under KRS 237.115.
So, it is not illegal, but it is not advised.
If you have your CDWL just conceal before entering the campus buildings or the grounds and you should be fine. I attend a public college, and I carry concealed every day.