Background
The pilot obtained a preflight weather briefing and filed a flight plan, but did not request any Notices to Air Missions (NOTAMs). As a result, the pilot was unaware that the destination airport was closed, as indicated by a NOTAM, until after the flight had departed.
Approach and Landing
During arrival, the pilot reported discovering an unplowed runway that appeared to have been used. Observing several tire tracks in the snow-covered surface, the pilot assumed the runway was open. The airport had no control tower or UNICOM facility.
The pilot executed an approach configured for a soft-field landing with full flaps. The aircraft touched down on approximately 8 inches of crusted snow. Almost immediately after touchdown, the nosewheel became buried in the snow, despite the pilot applying full up-elevator control.
Outcome
As the aircraft decelerated to about 10 knots, it rolled over onto its top. The sequence of events ended with the aircraft inverted.