According to the pilot, he departed McKinney (TKI), Texas, on a visual flight rules flight to Angel Fire (AXX), New Mexico. During the approach to AXX, the airplane encountered "extreme mountain turbulence" and the pilot "kept his speed up." Shortly after touchdown at AXX, the airplane "windmilled" to the left. The pilot then aborted the landing and during initial climb, the airplane's main landing impacted a snow bank located at the end of the runway. The main landing gear separated from the airplane, and the airplane remained airborne. The pilot then flew around the local area for an unspecified period of time and landed gear-up at Taos, New Mexico. During the gear-up landing at Taos, the airplane departed the runway surface and impacted the snow covered terrain. Examination of the airplane revealed the right aileron was bent and partially separated. The pilot and three passengers were not injured.