Capitalist with a generous welfare system is the proper term. But ironically, high taxes is also kind of a lie as people tend to only look at the highest rate of 50%, which you pay only if you earn more than €100,000/yr. Which in Denmark is a lot of money as stuff is cheaper than in the US. Most people pay between 20-30% income tax depending on region. All of that goes to the municipality, the county and the Church.
Denmark has a lot more taxes than america, but america wastes tax payer money on crap that does not help it's people a lot more than denmark does.
Also, Denmark is a monarchy, and socialists tend to dislike monarchies, so I am not sure if I would call denmark a socialist country.