Hello Mr. C. Pilot,
I have flow through Greenland three times on ferry flights many years ago: One Cessna 303, and two Twin Otters. It's spectacular, if you like desolation and beautiful topography. Mr. Ellsworth's advice is good though, it is not for the unprepared. The required survival equipment is expensive, and a minimum, if you end up needing it (as my ferry flying mentor did later in his career). Everything (fuel, landing fees, food & accommodation) are as expensive as you would expect to find, at an airport in the middle of nowhere, where there is no competition. There are no alternates when things go wrong. Each passing I did was amazing CAVU. If the weather had been poor, it would have been very intimidating.
My personal limit was to not accept flights in singles for Greenland flying. Nothing against singles but there's just not enough redundancy to let me relax with those huge distances of no place to even crash neatly. I've flown my single Cessna 60 miles off shore over sort of warm ocean water, and that is scary. Jump into ice cold water for even a moment, and you'll be glad for a brand new survival suit.
Most of the airports in Greenland simply do not have practical alternates for short range aircraft. It seems un-nerving when you file your alternate as your departure point! (and it's a sea away). The runways on the ice cap are useable by ski equipped aircraft only. The wheel planes which try apparently end up bulldozed off the end of the runway.
You could warm up with flying in Iceland. It is very beautiful, with wonderful people. It is not as stark, and not as unforgiving. I very highly recommend a flight to Heimaey Vestmannaeyjar, off the south coast of Iceland. It's amazing for walking.
There are also organized flights around the eastern Canadian arctic in the summer. These are a good choice, as you're with others, and there are many more choices if things go wrong.
Get lots of advice, and plan long and hard. If you go, do it safely, but you'll never forget it!
Cheers, Pilot DAR