Pilot reported loss of control and a runway excursion at RHP after landing and indicated poor runway condition may have contributed to the incident.

Narrative

The AWOS was reporting light winds down the runway with variable gusts of 15 knots up to a direct crosswind from the left. Well within the design parameters of this aircraft and my pilot experience. On short final; one of those direct crosswind gusts hit and I applied appropriate crosswind correction. When the airplane touched down on center line; the wheels contacted the runway individually with the upwind main wheel first; then the downwind main wheel; and then the nose wheel. The aircraft longitudinal axis was aligned with the runway centerline on touchdown. When the nose wheel touched down; the aircraft abruptly made an uncommanded turn to the right. I was able to prevent the runway excursion to the right using rudder/nose wheel steering and braking; but I was unable to prevent the excursion to the left. The airplane exited the runway onto the grass to the left of the runway. I was able to regain control of the aircraft and re-enter the runway and taxi to parking using the published taxiways with no further excursions. A post flight inspection showed no damage to the propeller; landing gear; fairings; or any other part of the aircraft.There was no damage to the runway; runway lighting; or any other non-aircraft property.Upon inspecting the runway; I found that there are many uneven; and damaged areas of the asphalt. Specifically on the runway centerline. It is uneven and exhibits many deep cracks. There are also holes in the asphalt between one quarter and one half inch thick. It is possible these defects may have contributed to the difficulty controlling the aircraft but it is unclear at this time.The cause of the excursion is not yet known. I have completed a full mechanical inspection with guidance from a qualified and competent aircraft mechanic familiar with this airframe and it was concluded that the airplane has no damage and is safe to fly.