Would it be weird to cold email former students of a prospective advisor?
This is an opinion and you may get opposite opinions, of course. If it is weird, it is only a little weird. I think it is something worth doing, actually. "How is Prof X to work with? Does s/he provide a lot of help or only a little. Any thing I should be aware of?"

There is very little worse in doctoral education than having a poor or abusive advisor. All you really need to know is that they treat students appropriately, even if they are (very) demanding. 

You can find a lot of horror stories about advisors by searching/browsing around this site. 

But just keep it informal. 

I don't recommend cold calling professors, but would treat calling students differently.