On June 3, 1994, approximately 0930 mountain daylight time, a Cessna 182H, N1838X, was substantially damaged during landing at Telluride, Colorado. The private pilot and two passengers were not injured. Visual meteorological conditions prevailed. The following is based on the pilot/operator report. En route, the pilot twice obtained weather reports for Telluride. Each report indicated the wind was calm. On final approach to runway 09, the pilot was advised the winds were from 130 degrees at 4 knots. During the flare, a gust of wind caused the airplane to increase altitude that was exaggerated by the runway downslope. The airplane "came down hard" and bounced. The pilot said she attempted to add power to go-around, but the engine did not respond because the propeller had been damaged by ground contact. The airplane landed "nose wheel first" and bounced several more times before coming to a stop. The nose gear and firewall were damaged.