The socialist government has often dominated Finland, but I have not noticed that they would try to limit the private ownership or anything else.
I think that you mean the communist system which restricts the freedom of the individual in many ways.
That's because you are confusing 2 separate things:
Capitalism and Socialism are economic systems.
A Republic and a Communist state are governmental systems.
A Republic can choose to have socialism as its economic system. In such a nation, people are socially free with minimal 'police force', while being economic slaves (extreme taxation for example). These type of coutries often tend to be prosperous despute being 'socialist' because they don't actually seek to aggressively enforce many of the ideas they officially endorse.
A Communist/Dictatorial government can choose to protect individual rights, and have a capitalistic economic system. To give you an example, China has gone from being EXTREMELY socialistic, to being largely a free economy. To the point that Coca-Cola's CEO explained that it is easier to start a business in China than it is in US. While such places DO exist, they often have an out of control government and social injustice (like enforcing one-child policy).
Finland is an example of a place where the government really doesn't enforce a whole lot of things because it doesn't need to. However, that doesn't take away from the fact that people there are not living in a free society.
To sum the whole thing up, free-market Capitalism (not crony-capitalism like US practices today) is a necessary condition for freedom. However, it is not a sufficient condition for freedom and requires a socially free society as well.