The pilot reported that while en route on the cross-country flight he noticed that the cylinder head temperature was rising. Suspecting a water leak through the cooling hose, he surveyed the remote area and made a precautionary landing on what appeared to be suitable terrain. After touchdown and during the landing roll the airplane encountered uneven ground, which resulted in the collapse of the nose landing gear and substantial damage to the airplane's right wing and empennage. In a written statement, the pilot reported that he should not have landed until he had located better terrain. The pilot reported no preimpact loss of engine power.