It's called an official visit because they are there on the invitation of the Icelandic President (and you can see that he and his wife accompanied the royal couple everywhere), just as they were e.g. in Schlesvig-Holstein on the invitation of the Minister President or in Romania on the invitation of the Romanian President.
If you would have a closer look at their agenda you would see that they visited certain places for certain reasons/purposes: they emphasize the connection between Iceland and DK.
It's called an official visit because they are there on the invitation of the Icelandic President (and you can see that he and his wife accompanied the royal couple everywhere), just as they were e.g. in Schlesvig-Holstein on the invitation of the Minister President or in Romania on the invitation of the Romanian President.
It's not a commercial/cultural mission like the trip to New York or to the EXPO in Japan or a trip related to a patronage like the one to Slovenia.
They are there to strenghten the bilateral relations with a country which once was a Danish colony (therefore the relation is sometimes a bit troubled) and still has many connections with DK. That's their work.
If you would have a closer look at their agenda you would see that they visited certain places for certain reasons/purposes: they emphasize the connection between Iceland and DK.
For example:
, thank you dear.
I know she wore this jacket for the photoshoot in the park at christmas last year. I don't know how to link the photos, sorry! But it is definately the same jacket.
I fully share your opinion. I have never paid much attention to this Crown Princely couple, but I shall do after this particular visit. Crown Prince Frederic and Crown Princess Mary truly enjoy each other company, respect each other, and feel comfortable together. I dare to say that this is what love is about...
The photos posted is a clear proof of the aforementioned. 
The schedule wasn't much different 4 years ago when the CP Couple of Norway was in Iceland on the invitation of the President (just not quite as tight since they had 6 month old Ingrid with them).
