Denmark is much better than Sweden, and Sweden is much better than Norway (in this regard only).
Denmark has a big market as far as I know, on "small" exotics, and exotic birds.
I don't have the exact laws, but I'm pretty sure they have more exotics allowed than Sweden.
Sweden is very simple - no carnivora (except for domestic dogs, cats, ferrets, and wild BADGERS), no wild birds, and no monkey and apes.
Slightly more complicated - it's said "primates" are banned, while the Ministry of Agriculture only specifies monkeys/apes (same word in Swedish - apa). Also, European native species of any animals I believe... as I'm sure you know, laws and regulations can be a maze.
But = no predatory mammals or birds, and no monkeys, unless you actually build a zoo.
In Norway, even zoos are banned, in theory, though some have special permission (dispens) to exist.
All reptiles and amphibians are banned, for decades, though 100 000 are kept illegally. The people in charge know this, but ignore it and keep the ban anyway. The ban is said to be "for animal welfare concerns", because "Norway's climate is not meant for reptiles". (It's brain-meltingly stupid, I know.)
It is definitely not an exotic-friendly country.
Iceland is an island of course, a very isolated one, and happy about it. No imported diseases or invasive animals, and they'd like to keep it that way, so importation laws even for domestic cats and dogs are extremely strict. I can't imagine them being happy about keeping even reptiles and parrots.
Edit: Now I read your full post, I'm very stressed today and just sped through the actual question before writing.
So you know a bit about Sweden, and yeah, I wouldn't recommend it. I've tried finding out about other European countries but it's hard (especially if you don't speak the language, and I'm only fluent in Swedish and English), me and hubby just want to go to the states. :p He asked if we should switch.