The short answer is that heavy metal happened to be exceptionally popular among these countries due to their strong infrastructure/education and the character of the music scene in the area.
The first clarification I have to make--you probably mean Nordic rather than Scandinavian, since Finland is not considered to be in Scandinavia. In fact, Finland's scene has historically been much larger than Denmark's.
The second is that sourcing for historical metal often takes the form of oral history. Metal is very new genre to the world of music and thusly many of the people who helped originate scene are still around. In addition, many academic sources fall short of analyzing metal due to their unfamiliarity with a general understanding of what is and what isn't metal, or they merely want to explore sociological conclusions rather than historical ones.
For a sociological perspective, Citylab released a study based on a graphic that was passing around using data from metal-archives.com, a website that catalogs and archives any band they consider to be 'metal.' Using this, somebody made a map that showed that the countries with the highest metal bands per capita were the Nordics, notably Norway, Sweden, Finland as well as Greece, Portugal, and Iceland. Central European countries also seemed to rank very high.
Citylab followed this us with a report that concluded that metal bands were more common per capita in countries with more wealth. This makes sense given that in order to be in a band, you need to have some level of access to musical knowledge and equipment. Countries with low levels of poverty and high levels of economic stability give people more access to both, and thus bands end up coming to fruition more often. A good example of this is Jon Nodtveidt of Dissection where in this interview he claims to have been playing guitar since he was eight or nine years old.
In the documentary "Until the Light Takes Us," a couple of the members of Norwegian black metal scene mention that they had early access to musical instruments in school, notably Fenriz of Darkthrone and Abbath of Immortal. Having access to these this sort of capital was crucial to helping shape a musical interest at a young age. Programs in school were widespread in Scandinavia/Finland, and that eventually allowed for more and more people to latch onto to musical performance in leisure time.
The second factor is that scenes in the older days, before the internet was widespread were much more locally influenced and attended. It was harder to hear a wide variety of bands when the only ones you had access to were extremely popular bands you could find at your local music store and then local bands. One local band that several musicians cite as influential is the band KISS (Until the Light Takes Us and Dayal Patterson's book, Evolution of the Cult, both mention them). KISS' style of heavy theatricality, obscene lyrics, and shocking live performance likely heavily contributed to heavy metal being as popular as it was, given it was also shocking and theatrical. And since the Nordic scenes were so insular and remote, bands were less likely to tour out there. The local music scene was likely the only outlet, and if there's a lot of bands out there that were playing heavy metal then it's easy to jump onto something that's also popular.
As for any non-material reasons why heavy metal itself became popular, that is anybody's guess. People have assumed the lack of sunlight during winter or greater issues with mental issues may have contributed, but based on the knowledge we have it's likely due to the fact that hard rock/heavy metal were popular forms of music at the time when young Nordic people started to get greater access to the means to play, create, and learn about music. Although it was never the major form of music, hard rock/heavy metal were a very popular subgenre by the late 70s and continued as such through the mid-late 80s. It may have just been chance that metal took as hold as much as it did.

Please consider reading Daniel Ekeroth's "Swedish Death Metal" and Dayal Patterson's "Black Metal: Evolution of the Cult" for further reading. They really go into the details of the developments of these scenes, and why in particular extreme metal really took hold in those countries.

Sources:
Aites, Aaron and Ewell, Audrey -Until the Light Takes Us (2008) Link
Ekeroth, Daniel - Swedish Death Metal (2008)
Florida, Ricahrd - How Heavy Metal Tracks the Wealth of Nations (2014)
Mudrian, Albert - Choosing Death: The Improbable History of Death Metal & Grindcore (2004)
Nodtveidt, Jon - Interview
Patterson, Dayal - Black Metal: Evolution of the Cult (2014)
Map of Metal Bands per Capita