Norway has one of the most equal societies in the world, Women are anything but submissive, they expect equality in all walks of life (and they generally get it).
They generally have better education than Norwegian men, in fact an issue is the number of lads that drop out of technical school. The law is such that they share childcare, as men are also entitled to paternity leave, a minimum of 6 week, but most take more as the majority of the parental leave (of up to a year) can be shared. You might not be able to get your American head round the concept of paid parental leave (80% of income for a year, or 100% for 10 months).
My boss will stay at home with the kids if they're ill and his wife has an important meeting to go to. The law requires at least 30% of board members to be women. The current government has a female finance minister, defense minister, transport minister, research and higher education minister, communities and regions minister, Trade and Industry minister, Children and equalities minister and Fisheries minister, around half of the cabinet positions.
My wife is Norwegian and whilst I would agree that they dress well and are beautiful, I can assure you that they aren't submissive, that we share the housework, cooking, cleaning and so on, she likes her wine, and only wears her Bunad on the 17th May.
Norway is not cheap, they have all the modern conveniences, sometimes more so than rural America, and are constantly rated at the top in the Human development Index by the UN.
You really do need to do better research.