We are a social democracy in the sense that the current political climate and consensus is shaped by a few decades of social democratic rule. High progressive taxes etc are seen as norm and are of course necessary to finance a large welfare state.
However: How the money for a large welfare state like the Nordic ones is raised is orthogonal to whether it's being spent on a large welfare state or not. Had we had 10% military spending we'd have a much smaller welfare state than today, with the same taxes.
It's entirely possible for a country to have a very large welfare state without being the least bit socialist - especially if they have natural resources. If the swedish national mining Company (yes, a state owned Company!) suddenly found resources allowing taxes to be halved - we would.
The Swedish mining company LKAB is a socialist (state-owned) enterprise, however the entire economy is not composed of socialist enterprises, therefore it is clearly a mixed economy.
Relatively high taxes on their own are not "social" or "socialist".
[1]http://www.thelocal.dk/20151101/danish-pm-in-us-denmark-is-n...
[1] http://www.thelocal.dk/20151101/danish-pm-in-us-denmark-is-n...