Being from Scandinavia myself, I very much doubt you will see pilot jobs available for non EU people - there is not a lack of qualified pilots within the EU.
Maybe if you are a doctor, engineer etc. you might have a chance - however Sweden are not able to do just as they wish anymore, as they are members of EU and Schengen.
Probably same strict rules as if anyone wants to go and work in the USA, pilots is a definate no go area, they will only accept you if you have a higher degree, doctor, nurse, teacher, engineer etc. - however pilots will not fall under this category.
Jobs in EU, must first be offered to EU citizens, if they still lack qualified personell then they are allowed to employ non EU personell.
As most people know, there is no lack of qualified pilots in europe at the moment. So work permit for non EU pilots, not a chance!