The first time two of your armed students mistook each other for potential killers and got into a shoot-out, the ridiculousness of that idea would be shown for what it is.
There are already specially trained individuals for the job: they're called police and they wear uniforms and carry weapons visibly so there will be no mistake about who they are or what they do. Maybe there should be more of them.
And what's so bad about closing campuses? Times have changed; security is tighter everywhere. Some students may well live in gated communities when they're at home -- so why not on campus?

I agree with all of Dennis Prager's points here, except the last. He writes, "(A)ll the recent university mass murderers were secular. Is this worth noting? . . . To nearly everyone in the media, the secularism of all the murderers is a non-sequitur." That's because it IS a non sequitur. Or, to be more precise, it is simply irrelevant.
In the first place, so-called "secularism" isn't even an "ism," per se. It's simply the default worldview of those who haven't been indoctrinated in the traditions, beliefs and dogmas of any religion. If I don't believe in the existence of leprechauns, does that make me an Anti-Leprechaunist?
Secondly, for thousands of years religious extremism has driven people to acts of violence, cruelty, brutality, torture, and mass murder, all committed expressly in the name of God. If it turned out that a campus killer had a strong belief in Christianity or Islam or Judaism, that fact WOULD be relevant and certainly worth noting. The absence of such beliefs is no more relevant than whether the killer was right- or left-handed, or what he had to eat for breakfast that morning.