@MacabreFoxWell, I got some good news... I think?
I looked it up, and there are a few ways to get free university education here in DK for free. I'll list up the rough versions.
1 - Participant in an Eramus Mundus program
2 - Exchange student
3 - People with a temporary... "thing-that-allows-you-to-stay-in-country" with the possibility of permanent stay.
4 - If you get a full stipend.
I can't tell you the details as I just don't know, but those are at least four possibilities. There's more to it, and I'm sure you could find out more if you looked it up.
Also, I went to class with a guy from America who was, as of yet, only on temporary stay (trying to get permanent to be with his wife and son), and I'm pretty sure he didn't pay a dime to study. It's only teacher's education (Seminariy, it's called, or teacher's training college according to google translate (yeah, we're both studying to become teachers)), but I think the same rules apply for this, as for university.