Suicide rates in Denmark: 10.6 out of 100,000 (making it number 40 out of the top countries for suicide). This puts it 44% below average. In comparison, the US is number 39 on the list, with rates of 11.1 per 100,000 people.
Denmark is number 36 in the world for length of life, being only a few years behind the leading countries and over four decades ahead of many others. The US is about equal.
Denmark has a relative poverty rate of 4.8%, a low rate. In comparison, the US has one of 15.1% (as well as having the largest gap between wealthy incomes and poor incomes, as well as between health benefits given to the rich compared to health benefits to the poor).
Out of 191 nations, Denmark is ranked by the WHO as:
65th in overall health (putting it in above about 66% of the rest of the world)
34th for health system performance (putting it above about 82% of the rest of the world)
28th for Disability Adjusted Life Expectancy (putting it above about 85% of the rest of the world)
21st for health distribution (putting it above about 89% of the rest of the world)
4th in the level of responsiveness (putting it above about 98% of the rest of the world)
3rd to 38th in the distribution of responsiveness (putting it above 80 to 98% of the rest of the world)
3rd to 5th in fairness of financial contribution (putting it above about 98% of the rest of the world)
20th at overall goal attainment (putting it above about 90% of the rest of the world)
So relatively, the Danes have low poverty and low suicide rates, while having high health and an effective and efficient health care system. All of which means that there’s no reason according to statistics to declare the Danes to be “unhappy” (heck, if any nation is unhappy, it would have to be the US according to some of these numbers). All of which fits in perfectly with people’s personal experiences in Danmark and with Danes.
So while saying that any nation is “happy” is somewhat meaningless, it seems that the Danes in general are as happy as anybody else, and a lot happier than many other nations.