I've never been in the situation, but from what I gather then both things happen. Sometimes your are given notice (and pay) but access revoked. But its also my understanding that in many cases, maybe even most, the employee works in the 3 months. The employer may even be a bit more lax with time off so the employee can do interviews with other companies. I know in most cases the notice period is used for handing over projects/work to another employee at the company, so stuff doesn't just get dropped. I get the security aspect, but from my experience its just not something an employee usually does. Maybe some other Danes can pitch in with their experiences.
I think its b/c getting fired is bad ofc, but not bad like in the US. I mean we have universal basic income, free healthcare etc. So I just don't think people feel pressured in a way that drives them to exploit access even after a notice, or get mad at the company in the same way. I'm just speculating. Again, there are companies and positions in companies where its a no brainer that access is revoked for security reasons.