The mystery is how the Eskimos crossed the rough Atlantic? They had only kayaks.
Physically you can cross it on kayak if lucky, but there is not much room to bring food on little kayak, and they would need to do it in a group, at least male and female.
They had umiaks also:
A large umiak can hold more than 20 people in its 6 metres (20 ft) to 10 m (33 ft) frame; and about seven skins are needed for the cover on a boat of 30 ft (9.1 m). It has traditionally been used in summer to move people and possessions to seasonal hunting grounds and for hunting whales and walrus.
http://en.wikipedia.org/wiki/Umiak
I'm not a sailor but reaching Norway from Greenland looks easier then reaching Hawaii from Polynesia:
The early settlement history of Hawaiʻi is still not completely resolved. Some believe that the first Polynesians arrived in Hawaiʻi in the 3rd century from the Marquesas and were followed by Tahitian settlers in AD 1300 who conquered the original inhabitants. Others believe that there was only a single, extended period of settlement.
http://en.wikipedia.org/wiki/Ancient_Hawaii#Voyage_to_the_Hawaiian_islands
Then we should not forget that Gulf Stream makes climate on the route from Greenland to Scandinavia much milder then in North Canada for example.
There is also a study from Helgason in 2000 which finds 7% of Q haplogroup in Iceland which could mean that Iceland was used as a temporary settlement for this people, but direct arrival to Scandinavia is also possible.
When discussing possibility of their arrival from opposite direction during migration period, as much as I know predominate Q1 subclade in Hungary (territory where Huns and Avars established their rule) is Q1a2, and in Scandinavia it is Q1a3. Also history did not record any such movement.