The pilot reported that prior to departing in a ski-equipped airplane, from a remote frozen, snow covered lake; he prepared the off-airport site by packing down the loose snow. During his takeoff roll, the left ski slid off the prepared surface, and encountered loose snow and water overflow which pulled the airplane hard to the left. The left wing struck a tree, substantially damaging the left wing. The pilot stated that there were no preaccident mechanical anomalies that would have precluded normal operation.