Okay, this will be difficult to answer for "Scandinavia" at large since the laws, and thus the legal and sometimes practical, status of women varied between countries, counties and cometimes even cities. I can answer for Sweden, for the most part.

On a very basic level, not much changed with the Christianization of Sweden in terms of women's rights. Under the country law of 1350 an unmarried woman was still under coverture of her closest male relative, usually the father, this the transfered to the husband when she married. A widow was of legal majority. In 1608 the old testament laws were formally written into law, however they were never enforced in practice which meant that when they were abolished a mere 78 years later very little changed in practice.

To complicate things a little further, the laws of Sweden were different between cities and the countryside. Basically two separate but similar laws. Generally speaking the situation for women was a little better in the cities in theory, particularly in terms of inheritance and legal right to education but in practice the limitations were usually more of social or economic character than legal.

In the countryside a woman was essentially expected to take part in the profession of her husband and by custom often acted independently within that profession. If widowed she had full legal right to remain active in the profession and generally speaking that right applied regardless of why the husband was absent. This custom becomes very clearly visible when studying the national situation during times of war when women, regardless of status, suddenly appear on legal documents, guild charters, tax documents and bascially everywhere else in society because the men were at war.

In the cities a daughter had equal inheritance to a son, (compared to half for the countryside) and legal right to primary education (but again, as previously stated, if you lived outside the city but could afford to attend school you were unlikely to be refused). Guilds, while often exclusively male in theory, frequently allowed female members in practice, usually wives or widows of guild members, and women were generally given the right to practice the same trade as the husband. There were some exclusively female guilds too, namely midwives and, to my knowledge uniquely in stockholm, rower women (Stockholm is built basically on the water with several major islands and waterway in addition to the archipelago and the large lake Mälaren, transporting people and goods was good business).

A Thousand Swedish Women's Years by Ohlander & Strömberg is really the magnum opus of women's history in Sweden. A really interesting read.

I'm hoping someone else can fill in the other scandinavian countries.