The pilot of the ski-equipped airplane reported that he aborted his first attempt to take off, and during his second takeoff in a tailwind, shortly after rotation, the airplane settled back onto the snow-packed runway. He further reported that the airplane lifted off again, but about 5 feet above the ground and near the end of the runway, a wind gust pushed the airplane down onto the runway. The airplane overran the runway and the right wing impacted a tree. The wind direction and speed were not discernable due to the lack of a windsock or weather reporting station. The airplane sustained substantial damage to the wings. The pilot reported that there were no preimpact mechanical failures or malfunctions with the airplane that would have precluded normal operation. The pilot chose to depart to the north due to raising terrain and tall trees on south end of runway. The airport elevation was approximately 7,600 feet with the runway length of 1,800 feet. The airplane owner's manual performance information for zero wind velocity and hard level surface recommends 3,260 feet for take of distance at 7,000 feet elevation, 40 degrees F. and flaps in the up configuration. With flaps at 20 degrees, the owner's manual recommends 3,420 feet for take of distance at 7,000 feet elevation and 40 degrees F. The owner's manual also identifies performance information for a skiplane under the most favorable condition of smooth packed snow at temperatures of approximately 30 degrees F, the skiplane take-off distance is approximately 10% greater than that shown for the landplane. However, via the Supplimental Type Certificate (STC) process the airplane did undergo an engine conversion to the 180 hp and constant speed propeller. No take-off performance data was identified on the STC. The pilot further reported he had landed and taken-off from this airport previously without incident.