Are there some seasonal activities, landscapes in which case my experience would be completely different if I would travel in Summertime or Wintertime?
That all depends on what you want to experience. Greenland is a very big country with a variety of climates and options.
South Greenland is best in the summer time, July or August and there you can experience the old Viking remains from a Viking culture that mysteriously disappeared in the 15th century. In Hvalsey you can find a church still standing where the last known event took place, a wedding September 16th 1408. When the next ship arrived they had all disappeared. Across from Narsarsuaq is Qassiarsuk where Erik the Red and Leif the Lucky lived 1.000 years ago. A replica of their farm Brattahlíð has been built. You can also take a beautiful walk to the ice cap, one beautiful route is through the valley of flowers from Narsarsuaq.
One of the most popular destinations in Greenland is Ilulissat, the fjord that produces more icebergs than any other in the world. There is a good variety of tourist services there including boat trips, dog sledding, helicopter tours and more.
One of my favorites is East Greenland, one of the least explored areas in the world. They still have blank areas on the maps which are simply marked "unexplored". It is a fantastic place to go dog sledding with the locals - where dog sledding is still their primary form of transport. Sermilik fjord is the second largest producer of ice bergs, but you will not go dog sledding at the same time as the ice bergs are on the move, as that is when the sea is frozen. The best time for dog sledding in March to May around Tasiilaq, but about a month later in Ittoqqortoormiit, which is further north at the mouth of the worlds largest fjord system, Ittoqqortoormiit. Both places, Tasiilaq and Ittoqqortoormiit are fantastic for kayaking in the summer time, particularly August and into September in Scoresby Sund and October in Sermilik fjord.
There are also great week long boat trips on an old sailboat offered in Scoresby Sund where you have the possibility of exploring the magnificent landscape with mountains rising over 3.000 meters up from the ocean, possible sightings of polar bears, walruses and several types of whale, and all surrounded by the world's largest glacier, the Greenland ice cap.
To get to Greenland you can either fly with Air Greenland from Copenhagen, or you can fly with Air Iceland from Reykjavik to several destinations in Greenland. The latter gives you the option of adding some Iceland experiences to the trip, which I see from your profile you are already familiar with :)
I know, it's a tough choice ;) If you give me some more info and what you would like to experience I can give you some more tips, but whatever you choose, it will be a trip of a life time.
Mentioned in this answer: