That's interesting. My Icelandic grandmother had an accent so I think I can "hear" what you are saying.
I'm not saying Iceland and Danish would necessarily be close to the same but I'm sure they might sound somewhat similar. When I hear a Scandinavian accent, I can't tell which country it comes from.
Similarly, the UK, Aus/NZ and even South African can be mistaken for each other.
If you were to travel to the US/Canada, you may think we all sound the same but can tell which part of Canada someone comes from when I hear them speak. There's quite a difference between Eastern/Western Canada but it's not quite as strong as the difference between the Northern and Southern US and East/West for that matter.
When we lived down south in Georgia, after a while I could tell the difference between Georgia/Alabama/Mississippi. I'm pretty sure Tennessee had it's own language.
The phrase most heard in those state - "You're not from around here, are you?" - each in their own local vernacular.