The pilot reported that while landing on a wet turf runway, the airplane began to skid. He initiated a go-around and then determined that he would not be able to clear the trees at the end of the runway. The pilot aborted the go-around and the airplane landed on the remaining runway, continued off the end of the runway, and impacted trees. The airplane came to rest upright on the ground in a grove of trees. The pilot reported that there were no preimpact mechanical failures or malfunctions that would have precluded normal operation. During the accident sequence an un-restrained passenger sustained a serious injury, and the airplane sustained substantial damage to the fuselage. The pilot stated that he provided the passenger a briefing on the use of the seatbelts before the accident; however, he did not confirm the passenger was wearing the seatbelts before landing. The passenger had unfastened the seatbelt during the flight.