In 2009 Greenland had 52,000 internet users, which are over 90% of the population. Greenland is connected via fiber-optic to Canada and Iceland.
Now, is 45-50% reach in case Facebook accounts something impressive? It isn't. Facebook's global average reach of **active** users is 44.5%.
> What special problems have they to solve (cold, snowstorm, bad visibility) to have good connection?
In Greenland there are no inland settlements, most of the population lives in the towns on the south-west coast.
> [...] according to this map [...] If these data are reliable
That's another issue. I don't think this map is reliable, as it shows many countries with FB usage way over 100% (with cases as extreme as 619% in Central African Republic or 505% in Iraq).