We study how local climate risk affects nationwide housing markets. We develop a dynamic spatial housing model with migration and property insurance channels, in which heterogeneous households choose location, housing tenure, and insurance coverage across regions differently exposed to climate shocks. The model generates realistic under-insurance and coverage heterogeneity across wealth, age, and regions, which interact with migration to determine climate risk exposure in the population. Our counterfactual experiments show, first, that housing prices endogenously reflect local risk and insurance costs where housing supply is imperfectly elastic. Therefore, the geographic distribution of households changes only slightly due to climate risk, suggesting that adaptation through migration has positive but limited benefits in equilibrium. Second, we evaluate popular insurance pricing policies designed to address the resulting rise in insurance costs and the protection gap. A subsidy to insurers that lowers the cost of high coverage and is financed by local homeowners meaningfully reduces climate risk exposure in the population. Alternative policies either increase exposure or generate large wealth transfers across regions.